Is 'charged black hole' an oxymoron?

[Dale]

Interesting. I will check if the same holds true in Schwarzschild spacetime.

 

[Naty1]

Austin0:

How would charge escape from the hole if light cannot?

[side comment: I think that's a question lacking proper perspective. For another thing, beside the above answer, a charged black hole will have more gravitational curvature due to the energy of the electromagnetic field.]

One view from Roger Penrose:

There is no mass as we know it (inside); inside all particles have been destroyed and gravitational effects remain outside the event horizon along with a few characteristics (electric charge, spin, etc).

from a loooong discussion in these forums [sorry, I did not save a link]

...the "source" of the observed EM field around a charged BH is the charge-current density in the collapsing matter; i.e., the observed field at any event in the exterior region is entirely determined by field propagation from charge-current density in the past light cone of that event.

[sounds like a PeterDonis, maybe??]

 

[PeterDonis]

[sounds like a PeterDonis, maybe??]

Yes, that was me, and yes, I was taking the same position that Penrose is taking in the quote from him. AFAIK that is the standard answer to the question "how does the charge get out of the BH?" (i.e., it doesn't have to), similar to the standard answer to the question "how does gravity get out of the BH?" There would also be an analogous question, "how does the angular momentum get out of the BH?", but for some reason nobody ever asks that one.

 

[Q-reeus]

I don't know Q-reeus. I have been going through the math for several days now, and I can show that the redshifting depends primarily on the rank and type of the tensor. Since charge and invariant mass are scalars (rank 0 tensor), the idea of either of them redshifting is, I think, incorrect. I am not quite done working on the math yet, but I don't think that any of the conclusions based on the idea that mass redshifts are going to be valid.

Good to know you've been beavering away on it DaleSpam! You are surely aware I and one or two others have been using 'redshift' in a loose way wrt mass/energy and charge. We know lowering any form of mass/energy of coordinate rest energy m down the potential well of some isolated massive body of rest energy M results in a net increase in gravitating mass to M+m√-g_tt, less than M+m owing to 'redshift' of m. Which can be more or less directly linked to the mass 'redshift'by in principle annihilating m or rather m√-g_tt and recovering the requisite redshifted radiation to infinity. The factor is the same regardless of tensor rank. E=hf makes the linkage rather good. As for charge, the huge problem with standard view is to reconcile that field energy does depress by redshift factor (non-free-fall case), yet field strength supposedly experiences no diminution whatsoever. Which btw also logically demands charge field lines remain exactly flat spacetime Coulombic in form regardless of how gravitationally warped things are for everything else. Strange indeed. No way I can see a sensible reconciliation without allowing effective charge screening as per last post. :zzz:

 

[Q-reeus]

Summary: the deBroglie wavelength [of a matter particle] redshifts just like light, except that with a matter particle it slows down while light maintains c locally while it redshifts.

There is some similarity but clearly not a 1:1 correspondence. A light ray will always outrun and outlast an outgoing particle whose local deBroglie wavelength goes infinite at it's turn-around point for instance.

 

[PeterDonis]

Interesting. I will check if the same holds true in Schwarzschild spacetime.

It looks like marcus was talking about the change in scale factor with expansion in FRW spacetime, and how it affects photons vs. massive particles. I'm not sure how relevant that will be to Schwarzschild spacetime, except for the general point that the observed energy of an object is the contraction of the object's 4-momentum with the observer's 4-velocity. But the particular effect marcus was talking about as "losing momentum relative to the CMB" does not happen in Schwarzschild spacetime because there is no expansion.

 

[Naty1]

PeterDonis:

It looks like marcus was talking about the change in scale factor with expansion in FRW spacetime, and how it affects photons vs. massive particles. I'm not sure how relevant that will be to Schwarzschild spacetime,

Correct regarding Marcus. I edited my post above to highlight FLRW spacetime.

...the particular effect marcus was talking about as "losing momentum relative to the CMB" does not happen in Schwarzschild spacetime because there is no expansion.

exactly...I did not know Dalespam was working in Schwarzschild coordinates; On the other hand redshift is redshift, gravitational or 'expansion distance based', so it will be interesting to see if anything worthwhile appears.

Is this the issue where it was recently discussed 'why free fall has no redshift' or somesuch?? I just realized that might be where this discussion resides...I don't recall those coordinates. Sorry if I detoured the discussion.

 

[PeterDonis]

Is this the issue where it was recently discussed 'why free fall has no redshift' or somesuch??

No, that's this thread:

https://www.physicsforums.com/showthread.php?t=613902

We've covered some of the same ground here, but with a different focus.

 

[Dale]

We know lowering any form of mass/energy of coordinate rest energy m down the potential well of some isolated massive body of rest energy M results in a net increase in gravitating mass to M+m√-g_tt, less than M+m owing to 'redshift' of m.

I don't know that, do you have a reference or derivation?

I am also not sure of the relevance to most of the thought experiments proposed here, which have seemed to focus on test masses and charges interacting with each other rather than altering the field of the gravitating mass. I think that assuming the two things are equal is sketchy.

 

[PeterDonis]

We know lowering any form of mass/energy of coordinate rest energy m down the potential well of some isolated massive body of rest energy M results in a net increase in gravitating mass to M+m√-g_tt, less than M+m owing to 'redshift' of m. Which can be more or less directly linked to the mass 'redshift'by in principle annihilating m or rather m√-g_tt and recovering the requisite redshifted radiation to infinity.

I see DaleSpam has commented on this as well; this way of putting things conceals a lot of interpretation of ambiguous terms. We've gone into this in previous threads, and somewhat in this one, but perhaps it's worth some further comments to capture the thoughts I've come up with:

Suppose I am "hovering" at some large distance above a Schwarzschild black hole, and I measure its mass, M, by putting test objects into orbits about the hole, measuring their orbital parameters, and applying Kepler's Third Law. Then I drop an object of mass m, where I determine m locally by some similar procedure, into the hole. (All objects so far are electrically neutral; I'll talk about the charged BH/charged object case later in this post.) There are at least three possible ways I can do this:

(1) If I just let the object free-fall into the hole, and it doesn't give off any radiation, then the hole's mass, measured by me in the same way as before, will increase by m.

(2) If I slowly lower the object into the hole, extracting work from the process as I do so, then I can make the mass increase of the hole as small as I want by lowering the object closer and closer to the horizon before I finally have to release it and let it free-fall the rest of the way. In principle, how close to the horizon I can lower the object and still extract work depends on how I lower it and the strength of the materials I use to do so; ultimately it depends on what (finite) proper acceleration the lower end of the mechanism for lowering, the one attached to the object, can withstand. The final mass increase of the hole, for an idealized process where I extract the maximum amount of work possible while lowering the object to some radius r > 2M, will be m \sqrt{1 - 2M / r}.

(3) If I let the object free-fall towards the hole, but at some radius r > 2M, I capture all its kinetic energy and convert that to outgoing radiation (say, for example, it hits a large mirror which stops it, converts its kinetic energy into heat, and then reflects all the heat outward as it radiates away), I can in principle make the mass increase of the hole as small as I want, just as in #2 above, by moving the stopping point closer to the horizon. The only difference, from my point of view, is that I am now not capturing the difference between m and m \sqrt{1 - 2M / r} as work; it's just radiating away as heat.

There's another subtle point about the above three scenarios: how do we define the "energy at infinity" present? The three applicable quantities are the Komar mass, the ADM mass, and the Bondi mass. Here's how I see those for the three scenarios above (all three scenarios assume that all masses except that of the hole and the object dropped/lowered in are negligible):

Starting state: all three masses are M + m. Mass M is the hole, mass m is the object we're about to drop/lower in, which is at some finite radius so all three masses will include it.

#1: All three are unchanged; the only change is that M + m is now all contained in the hole.

#2: All three are unchanged: the only change is that M + m \sqrt{1 - 2M / r} is contained in the hole, and the remainder of m is still at our finite radius, where we recaptured it as work extracted from the lowering process.

#3: The ADM mass and Komar mass are still M + m; however, the Bondi mass is now decreased to M + m \sqrt{1 - 2M / r}, the new mass of the hole, because it will not include the mass (energy) of the radiation that escaped to infinity.

Now, suppose we do similar experiments to the above, but with a charged (R-N) black hole and a charged object. We have two possible cases, opposite charges and like charges. I am not presently working the math in detail as DaleSpam is, but it looks to me like the following are key points:

First, there should be a sort of ADM charge/Komar charge/Bondi charge for the spacetime as a whole, definable similar to the way the corresponding masses are defined. For the case we're considering, this total would include *both* the charge Q of the hole *and* the charge q of the object that's going to be dropped or lowered in. We, at a large finite radius, would measure the charge Q of the hole using charged test objects, similar to the way we measured its mass M by Keplerian orbits; we would also locally measure the charge q of the object to be dropped/lowered in similar to the way we measured its mass m locally.

Second, at the starting state, all three of the ADM/Komar/Bondi charges should be equal, just as the masses are; they should all be Q + q. However, at the end state for *any* of the three scenarios, *all three* charges should still be unchanged, *unlike* the case for masses above. This is because there is no way to radiate charge "away to infinity" as we can with mass by converting it into radiation. This is a key difference between mass and charge. (Note: it *is* possible for the charge q of the object dropped into cancel some or even all of the charge Q of the hole. However, if that is the case, all three of the ADM/Komar/Bondi charges *already* comprehend that; they already "see" the net charge, Q + q, which will be less than Q if q is of opposite sign.)

Third, if the object I am going to drop/lower into the hole is charged, then there is an extra energy e present in the spacetime as a whole, i.e., in the starting ADM/Komar/Bondi energy, due to the extra potential energy due to the charges Q and q being separated. So the total starting energy is M + m + e.

Note that as I've just defined it, e is positive if Q and q are of opposite sign--in this case, if I do a process like #2 or #3 above, I can in principle capture up to m + e of energy as work, or have that much energy radiate away to infinity, instead of it going into the hole. The final mass of the hole will be M + (m + e) * sqrt(1 - 2M/r), where r is the radius of the "stopping point", with the remainder of m + e captured as work or radiated away to infinity. The ADM/Komar mass will not change, and the Bondi mass will decrease to the new mass of the hole.

If Q and q are of the same sign, e will be *negative*. Depending on how large e is compared to m, it may be possible to do processes #1, #2, or #3 above, but capturing less energy than m (instead of more, as above); or it may not be possible to do them at all, because the electrical repulsion between the hole and the object is enough to require work to be *added* to the object to make it fall below the horizon.

Sorry for the long post, but I wanted to get all that down while it was fresh in my mind.

 

[Trenton]

As I understand it, it's actually very difficult for a black hole to acquire a significant charge. A positively charged black hole would repel any protons near it, so those protons would have to be fired inwards with a very high kinetic energy to overcome the electrical repulsion. If absorption is achieved, the kinetic energy contributes to the mass of the black hole (via E=mc²), and eventually you reach a point where each proton adds more mass than charge. Therefore it's postulated (I think) that the two horizons might never meet.

DrGreg,

I too have heard this but I am not sure quite how to view it. If, due to infall of space, nothing can be at rest inside the outer horizon because to do so would mean it was, in effect, traveling outwards at greater than C, then how can a charged particle do it? How indeed can a charged particle ever experience an electric field until it got to the singularity. Or is it that a charged black hole does not have a singularity but a dense entity bound by the inner horizon?

This last point arises from the idea that a spinning BH has a ring singularity. Spin distorts from a point to a ring. Charge if it distorts at all must be to a sphere - The only problem with that is it is no longer singular. One way at least to erradicate the naked singularity!

 

[PeterDonis]

there should be a sort of ADM charge/Komar charge/Bondi charge for the spacetime as a whole, definable similar to the way the corresponding masses are defined.

Having run some formulas, let me be more definite about what I was proposing in the above quote. I emphasize that I have not seen this in any standard literature in this form, although what I'm proposing for the "ADM charge" is basically Gauss's law in integral form, slightly rewritten and taken to an appropriate limit.

(1) ADM charge: the integral for the ADM mass can be expressed as follows (note that I am leaving out constant factors involving pi and so forth, I'm only trying to look at the structure of the formulas, not give exact results):

M = \lim_{S \rightarrow i^{0}} \int g^{uv} \left( g_{ua, v} - g_{uv, a} \right) n^{a} d S

as given, for example, in this paper (which I believe references some of the original ADM papers):

http://arxiv.org/pdf/gr-qc/0609079v1.pdf

But we can rewrite this in a more general form:

M = \lim_{S \rightarrow i^{0}} \int m_{a} n^{a} d S

m_{a} = g^{uv} \left( g_{ua, v} - g_{uv, a} \right)

where now we have clearly separated out two distinct things: (1) defining a 2-sphere surface dS with outward pointing normal n^{a}, which we will then "take to infinity" in the limit; and (2) defining a 1-form m_{a} that represents "what we want to integrate" over the 2-surface. We will define "ADM charge" by keeping (1) the same but varying (2).

In the case of the ADM mass, what we are integrating over the 2-surface is basically the effect of the "mass" inside the surface on the metric at the surface. For charge, we want to integrate the effect of the charge inside the surface, over the surface. But we know how to do this: it's just Gauss's law. All we need to do is define a 1-form representing the "lines of force" going through the surface, which will be defined by the electric field normal to the surface. So we can write:

Q = \lim_{S \rightarrow i^{0}} \int F_{a0} n^{a} d S

This is basically Gauss's law, expressed in the "Schwarzschild" type coordinates we have been using for the R-N metric, taken to the limit at spatial infinity. But there's still one flaw: we've picked out a specific component of the EM field tensor, the "0" component. We can make the formula invariant by using the timelike Killing vector field of the spacetime, which will pick out the same "0" component in Schwarzschild coordinates, but which now allows the formula to be generalized to any chart, just like the ADM mass formula:

Q = \lim_{S \rightarrow i^{0}} \int F_{ab} n^{a} u^{b} d S

where u^{b} is a timelike unit vector (in this case, the "time translation" unit vector of R-N spacetime). It looks to me like, modulo constant factors, the value of this integral should equal the "Q" parameter in the standard R-N metric. I'll work on checking that explicitly.

(2) Komar charge: Actually, what I just wrote down above should *be* the Komar charge, as well as the ADM charge, because the "use a timelike vector field to make the integral formula invariant" trick is the same trick that's used for the standard Komar mass formula. There is one wrinkle: I haven't written down any analogue to the stress-energy tensor for charge. I think there's a way to finesse that by using Maxwell's equations to equate the expression F_{ab} n^{a} u^{b} to an expression involving the charge-current 4-vector. But I need to check that as well.

(3) Bondi charge: The formula for this would look the same as for the ADM charge, except that the limit would be taken as S goes to future null infinity instead of spatial infinity. Since there is no way for charge to radiate away to infinity, as I said before, this does not change the result at all, so Bondi charge = ADM charge.

Edit: Changed to timelike unit vector field in the above formulas (instead of timelike Killing vector field).

 

[Austin0]

Austin0:

How would charge escape from the hole if light cannot?

[side comment: I think that's a question lacking proper perspective. For another thing, beside the above answer, a charged black hole will have more gravitational curvature due to the energy of the electromagnetic field.]

You may be quite right about perspective but your comment was a little indefinite to be really helpful ;-)

One view from Roger Penrose:

There is no mass as we know it (inside); inside all particles have been destroyed and gravitational effects remain outside the event horizon along with a few characteristics (electric charge, spin, etc).



...the "source" of the observed EM field around a charged BH is the charge-current density in the collapsing matter; i.e., the observed field at any event in the exterior region is entirely determined by field propagation from charge-current density in the past light cone of that event.

Could you elaborate on this concept of field propagation from past light cone?
_
Thanks_________________

 

[PeterDonis]

Could you elaborate on this concept of field propagation from past light cone?

I believe Naty1 got this from me originally; it actually came up in another thread earlier today, and I posted this:

https://www.physicsforums.com/showpost.php?p=3965324&postcount=17

It talks about gravity, not charge, but the reasoning for charge is similar; the only difference is that the "source" that has to be somewhere in the past light cone is the charge-current density 4-vector (the source in Maxwell's equations) instead of the stress-energy tensor (the source in the EFE).

 

[PeterDonis]

I haven't written down any analogue to the stress-energy tensor for charge. I think there's a way to finesse that by using Maxwell's equations to equate the expression F_{ab} n^{a} u^{b} to an expression involving the charge-current 4-vector.

I should have seen this one at once; it's just the generalized Stokes Theorem plus Maxwell's equation with source. We have:

\int F_{ab} n^{a} u^{b} dS = \int \nabla_{c} F_{ab} g^{ac} u^{b} dV = \int J_{b} u^{b} dV

where it's technically the charge-current 1-form instead of the vector appearing, but that's a minor point. The only other potential issue is how to properly define the integration measure; I think there should be a \sqrt{-g} somewhere in there, but it may be that the appearance of the charge-current 1-form instead of the vector already implicitly takes that into account. But in any event I believe this shows how the "Komar charge" integral does in fact connect back to the source of the EM field, just as the Komar mass integral connects back to the source of gravity.

 

[Austin0]

I believe Naty1 got this from me originally; it actually came up in another thread earlier today, and I posted this:

https://www.physicsforums.com/showpost.php?p=3965324&postcount=17

It talks about gravity, not charge, but the reasoning for charge is similar; the only difference is that the "source" that has to be somewhere in the past light cone is the charge-current density 4-vector (the source in Maxwell's equations) instead of the stress-energy tensor (the source in the EFE).

so we would have to go a billion years into the Earth's past light cone to find the "source" of the gravity the Earth feels at this instant--but the gravity itself, the effect, would be the same if the Sun's mass were the same, because the way the field from the collapsing object "propagates" through the empty vacuum region outside it is static--it stays the same for all time (again,

The basic past light cone analogy is self evident wrt the Earth-Sol system.
But if an electromagnetic or gravitational field is dependent on propagation, renewal from charged particles or mass, then the idea of a static propagation is a little obscure.
this would seem to imply that if the mass was moved somehow, the field could remain behind independent of a necessary source.
In the case of gravity it makes sense that the field would still be there. Possible that gravity itself is somehow exempt and still could emanate from the mass. But with charge, as Penrose said the source of charge , particles no longer exist at that point so the idea of a field remaining, extending to infinity with no source whatever is hard to understand.
As you might guess I am just starting to pay attention to black holes ;-)

 

[PeterDonis]

But if an electromagnetic or gravitational field is dependent on propagation, renewal from charged particles or mass, then the idea of a static propagation is a little obscure.
this would seem to imply that if the mass was moved somehow, the field could remain behind independent of a necessary source.

If the mass is moved, its "arrangement" in everybody's past light cone will change as the information about the move propagates to them. That changes the observed field.

In the particular case we've been discussing, that effect is obscured because the spacetime is static; nothing changes with time. In a more realistic, dynamic spacetime, the field observed at a given point would change with time, as dynamic information about the movement of masses elsewhere propagated around.

In the case of gravity it makes sense that the field would still be there. Possible that gravity itself is somehow exempt and still could emanate from the mass.

No, gravity isn't exempt. But the mass it's "emanating" from isn't inside the black hole.

If you want to view the field at a given point in space, outside the hole, as "emanating" from something, then it is emanating from portions of the collapsing matter far in the past, closer and closer to the horizon; as the collapsing matter far in the past gets closer and closer to the horizon, the time delay for light signals from it to get out to some fixed radius increases without bound. So the gravity you are sensing now "emanates", if you want to look at it that way, from some small piece of the collapsing matter's worldline, say, 10 meters above the horizon; the gravity you will sense some time in the future will have emanated from a small piece of the collapsing matter's worldline, say, 9 meters above the horizon; and so on.

In the case of a static spacetime (after the hole forms), the "emanating" view just above is equivalent to the "static" view, where once the collapsing matter falls inward past a certain radius, the field at that radius becomes fixed for all future time. But in a dynamic spacetime, there is no "static" view, so yes, you would need to look for dynamic information about the movement of mass traveling around.

But with charge, as Penrose said the source of charge , particles no longer exist at that point so the idea of a field remaining, extending to infinity with no source whatever is hard to understand.

The same thing I said above goes for charge; it emanates from charge-current density in the past just as gravity emanates from stress-energy in the past. Gravity "extends to infinity" just as charge does; the mass of any gravitating body leaves an "imprint" on the spacetime far away. Even if the gravitating body collapses to a black hole, the "imprint" of its mass on the spacetime remains the same, because the imprint doesn't come from inside the hole; it comes from the past, before the object disappeared behind the horizon, as described above. The "imprint" of charge on the spacetime works the same way. Even if there is no charge-current density inside the black hole (or any nonzero stress-energy), since it's all been destroyed in the singularity, there is still charge-current density (and stress-energy) in the past.

The ADM, Komar, and Bondi masses I talked about in recent posts are ways of describing the "imprint" of mass on the spacetime far away; the similar stuff I proposed for charges captures the same thing.

 

[Q-reeus]

Q-reeus: "We know lowering any form of mass/energy of coordinate rest energy m down the potential well of some isolated massive body of rest energy M results in a net increase in gravitating mass to M+m√-gtt, less than M+m owing to 'redshift' of m. Which can be more or less directly linked to the mass 'redshift'by in principle annihilating m or rather m√-gtt and recovering the requisite redshifted radiation to infinity."

#3: The ADM mass and Komar mass are still M + m; however, the Bondi mass is now decreased to M + m√(1−2M/r), the new mass of the hole, because it will not include the mass (energy) of the radiation that escaped to infinity.

Well I had hoped it would have been evident this definition is what was being implied in bit quoted - we are obviously discounting as gone from considered system energy extracted in lowering (and 'lowering' was deliberately the term used) mass m. All btw covered in #1.

Now, suppose we do similar experiments to the above, but with a charged (R-N) black hole and a charged object. We have two possible cases, opposite charges and like charges. I am not presently working the math in detail as DaleSpam is, but it looks to me like the following are key points:

First, there should be a sort of ADM charge/Komar charge/Bondi charge for the spacetime as a whole, definable similar to the way the corresponding masses are defined. For the case we're considering, this total would include *both* the charge Q of the hole *and* the charge q of the object that's going to be dropped or lowered in. We, at a large finite radius, would measure the charge Q of the hole using charged test objects, similar to the way we measured its mass M by Keplerian orbits; we would also locally measure the charge q of the object to be dropped/lowered in similar to the way we measured its mass m locally.

Second, at the starting state, all three of the ADM/Komar/Bondi charges should be equal, just as the masses are; they should all be Q + q. However, at the end state for *any* of the three scenarios, *all three* charges should still be unchanged, *unlike* the case for masses above. This is because there is no way to radiate charge "away to infinity" as we can with mass by converting it into radiation. This is a key difference between mass and charge. (Note: it *is* possible for the charge q of the object dropped into cancel some or even all of the charge Q of the hole. However, if that is the case, all three of the ADM/Komar/Bondi charges *already* comprehend that; they already "see" the net charge, Q + q, which will be less than Q if q is of opposite sign.)

All that and your later points pretty well makes perfect sense *if* one starts off with the assumption of an RN BH that acts externally as a charged object - which however is what this thread set out to seriously question. I gave an updated argument involving effective charge screening in #248 which imo provides a level of conceptual consistency lacking in standard RN picture, as one or two of the bizarre consequences pointed out in #254 were meant to highlight. In fact apart from that added thought in #248 nothing substantially new has been added since #1 really. So I don't know, in the end it may simply come down to another fizzle/fadeout which at bottom amounts to "concensus/majority opinion ruulz - OK!" But no - sour grapes premature at this point.

 

[PeterDonis]

All that and your later points pretty well makes perfect sense *if* one starts off with the assumption of an RN BH that acts externally as a charged object - which however is what this thread set out to seriously question.

Well, everything I said would apply equally well to a charged massive object like a planet or star; DaleSpam recommended earlier that we start with that case, which avoids potential issues with what happens at or inside the R-N BH horizon, and if you're having problems with the BH case I would agree with his recommendation. The only difference with a planet or star vs. a BH is that the minimum radius r that you can lower something to is quite a bit larger than the horizon radius. But the ADM/Komar/Bondi charges I defined, just like their mass counterparts, are perfectly well-defined for a charged massive object, so they don't depend on having an R-N BH; they only depend on the exterior vacuum spacetime geometry of a charged massive object being R-N, i.e., only on R-N geometry outside some radius r greater than the horizon radius for the given mass and charge. I think the latter assumption is pretty safe.

 

[PeterDonis]

a level of conceptual consistency lacking in standard RN picture, as one or two of the bizarre consequences pointed out in #254 were meant to highlight.

In #254, you say:

the huge problem with standard view is to reconcile that field energy does depress by redshift factor (non-free-fall case), yet field strength supposedly experiences no diminution whatsoever.

I'm not sure what you mean by "field strength...experiences no diminution". Go back to scenario #2 in my previous post with a charged object, charged oppositely to the hole. The ADM/Komar/Bondi charge "at infinity" is Q + q always; but by hypothesis, you, at your finite radius, before you lower the charged object, see a field strength based on Q, *not* Q + q. After the object is lowered, you now see a reduced field strength, based on Q + q, which is less than Q, because that is now the charge you see on the hole. (Again, for "hole" read "central charged massive object" if that works better, see my previous post.)

Also remember that when you say "field energy does depress by redshift factor", what you really mean is that you are *extracting* energy from the lowering process. Where is that energy coming from? From the energy "at infinity" m + e of the charged object you are lowering. It does *not* come from the "energy of the hole", so it does not come from the "field energy" associated with the hole's charge Q. It comes only from "field energy" that is present because there is a second, opposite charge, q, which started out separated from Q, and then you brought them together. I don't see any problem or inconsistency anywhere in this.

 

[GAsahi]

The motion of charged vs uncharged particles.

How would the electro(static) field propagate past the EH? Photons don't, how would virtual photons (the carriers of em field) ?

 

[Q-reeus]

Q-reeus: "the huge problem with standard view is to reconcile that field energy does depress by redshift factor (non-free-fall case), yet field strength supposedly experiences no diminution whatsoever."

I'm not sure what you mean by "field strength...experiences no diminution". Go back to scenario #2 in my previous post with a charged object, charged oppositely to the hole. The ADM/Komar/Bondi charge "at infinity" is Q + q always; but by hypothesis, you, at your finite radius, before you lower the charged object, see a field strength based on Q, *not* Q + q. After the object is lowered, you now see a reduced field strength, based on Q + q, which is
less than Q, because that is now the charge you see on the hole. (Again, for "hole" read "central charged massive object" if that works better, see my previous post.)

Chalk and cheese comparison imo. Your point here amounts to simply that opposite charges cancel which of course I agree with. At question is the effective coordinate value of charge as a function of gravitational potential - a different matter entirely.

Also remember that when you say "field energy does depress by redshift factor", what you really mean is that you are *extracting* energy from the lowering process. Where is that energy coming from? From the energy "at infinity" m + e of the charged object you are lowering. It does *not* come from the "energy of the hole", so it does not come from the "field energy" associated with the hole's charge Q. It comes only from "field energy" that is present because there is a second, opposite charge, q, which started out separated from Q, and then you brought them together. I don't see any problem or inconsistency anywhere in this.

This is now a very long thread so won't bother to try and quote previous posts but one can get the point without resorting to a lowering process per se. Start off with closely spaced charges already at a lower potential and separate then transversely to form a dipole p. We do I trust agree that the energy required to form said p is less by the redshift factor than if same operation is performed 'out there'. That's reduced stored field energy, and yet if any electric field whatsoever can be perceived externally to an EH, the infinite redshift existing there logically demands no gravitational diminution of field strength is possible - period. As I have said repeatedly in earlier posts. So Peter - kindly offer please your synthesis of those two facts (or at least one firm fact and one supposed 'fact').

 

[PeterDonis]

At question is the effective coordinate value of charge as a function of gravitational potential - a different matter entirely.

It's not unrelated, because whatever geometric object describes the charge of the object being lowered, it must behave differently in some respects as a function of radius than the object's 4-momentum, which describes its energy, because the energy can be extracted as work or radiated to infinity, but the charge can't. I suggested in an earlier post that this would be reflected by the charge-current 4-vector always being parallel transported along the object's worldline, while the 4-momentum would only be parallel transported if the object traveled on a geodesic, i.e., if it was freely falling; for my case #2, an object being slowly lowered with work extracted, the 4-momentum would *not* be parallel transported. (My case #3 would ultimately work the same--the 4-momentum would be parallel transported while the object was freely falling, but would then undergo a very sudden non-parallel-transport change when the object hit the mirror at the bottom and its kinetic energy was converted into outgoing radiation.)

Start off with closely spaced charges already at a lower potential and separate then transversely to form a dipole p. We do I trust agree that the energy required to form said p is less by the redshift factor than if same operation is performed 'out there'.

No, I'm not sure we agree on that. For energy measured locally, it's the same regardless of where you do the experiment, by the equivalence principle. For energy measured "at infinity", I'm not sure; I would have to work through the math.

 

[Q-reeus]

It's not unrelated, because whatever geometric object describes the charge of the object being lowered, it must behave differently in some respects as a function of radius than the object's 4-momentum, which describes its energy, because the energy can be extracted as work or radiated to infinity, but the charge can't. I suggested in an earlier post that this would be reflected by the charge-current 4-vector always being parallel transported along the object's worldline, while the 4-momentum would only be parallel transported if the object traveled on a geodesic, i.e., if it was freely falling; for my case #2, an object being slowly lowered with work extracted, the 4-momentum would *not* be parallel transported. (My case #3 would ultimately work the same--the 4-momentum would be parallel transported while the object was freely falling, but would then undergo a very sudden non-parallel-transport change when the object hit the mirror at the bottom and its kinetic energy was converted into outgoing radiation.)

Agreed that unlike energy ('gravitating charge' in effect) one cannot radiate away charge, but consider my commentary in #17 to be an appropriate reflection on that.

No, I'm not sure we agree on that. For energy measured locally, it's the same regardless of where you do the experiment, by the equivalence principle. For energy measured "at infinity", I'm not sure; I would have to work through the math.

Sorry I neglected to specify the energy redshift was a coordinate measurement, but thought that would be taken for granted. We have worked through numbers of equivalent such situations here and can honestly see no room for doubt over what is a pretty simple and straightforward scenario. It is nothing more than an application of what we both agreed to surely in e.g. #254 or situation #3: in your #260 - adapted to finite potential drop. As the 'test charges' are clearly to be treated as a minor perturbation to a far greater central mass there surely is no thought of any significant alteration to Schwarzschild metric. Why would one then expect other than that the rather localized dipople electrostatic field energy would redshift any differently to a lump of neutral matter? :zzz:

 

[DrGreg]

If, due to infall of space, nothing can be at rest inside the outer horizon because to do so would mean it was, in effect, traveling outwards at greater than C, then how can a charged particle do it?

A charged particle approaching a charged black hole would experience repulsion before it reached the outer horizon. If it was going fast enough to cross the horizon it would never escape, as by then the gravity would be stronger than the repulsion (to borrow Newtonian language).

How indeed can a charged particle ever experience an electric field until it got to the singularity.

Other posts in this thread (e.g. #264, #267) have been discussing that the charged particles that originally fell into the hole in the past (to charge it) still leave an electromagnetic field behind them, outside the horizon, which "can't escape fast enough", to put it rather crudely.

 

[PeterDonis]

Agreed that unlike energy ('gravitating charge' in effect) one cannot radiate away charge, but consider my commentary in #17 to be an appropriate reflection on that.

But your commentary in #17 does not even address the key difference: the *reason* that energy "redshifts" in the scenario where an object is slowly lowered is that energy is being *extracted* during the process. There is no way to correspondingly "extract charge" from a charged object that you are slowly lowering.

As the 'test charges' are clearly to be treated as a minor perturbation to a far greater central mass there surely is no thought of any significant alteration to Schwarzschild metric.

So your intent in this scenario was to create a dipole from a pair of oppositely charged test objects hovering above a *neutral* BH? I had thought you meant to have them above a charged BH (or a charged planet/star).

Why would one then expect other than that the rather localized dipople electrostatic field energy would redshift any differently to a lump of neutral matter? :zzz:

It would seem to me that the following would be true, anyway: if the work needed to create the dipole is done locally, the amount of work will be the same regardless of where in spacetime the dipole is created. Call that work W. If, however, the work is done elsewhere and "transmitted" to where the dipole is formed (say, for example, that the charged objects are pushed apart by a gear mechanism, and the mechanism is driven by a linkage that reaches down from a higher altitude), then at the higher altitude where the work is generated, the amount of work needed will indeed be "redshifted"; it will be less than W. But if the work done locally by the gear mechanism is measured, it will be W; as the work is transmitted down the linkage, it "blueshifts" back to its local value. That would be true of any scenario where work is transmitted from a higher to a lower altitude.

As far as "charge redshifting" is concerned, I see what you are saying: viewed from the higher altitude, the energy stored in the dipole is less than W, but the separation of charges is the same (since it's tangential), so it looks like the charges must be reduced. But this can equally well be interpreted as the effect of the curved spacetime in between, rather than anything intrinsic to the charge. After all, locally the dipole has stored energy W, so whatever change is seen from a distance would seem to be due to the intervening spacetime.

We've had this discussion before, of course; I don't see that this scenario is any different from the other ones where we've had it. You are trying to assign a meaning to "how things look from a distance" that is not necessary. It's not that it's "wrong", exactly; just that it's not necessary, you can do all the physics and interpret all the physics without it, so it's just your personal way of viewing things, IMHO.

 

[Dale]

How would the electro(static) field propagate past the EH? Photons don't, how would virtual photons (the carriers of em field) ?

Easy, virtual photons are off-shell, meaning they can travel faster than c and even have mass.

 

[Dale]

Well I had hoped it would have been evident this definition is what was being implied in bit quoted - we are obviously discounting as gone from considered system energy extracted in lowering (and 'lowering' was deliberately the term used) mass m. All btw covered in #1.

So, let me see if I correctly understand your chain of reasoning.

1) There exist three global measures of mass that could be considered in an asymptotically flat and static metric. Out of those three you equate the Bondi mass with the M parameter of the Schwarzschild metric.
2) You note that the Bondi mass "redshifts" in the specific case where energy is radiated to null infinity. You then generalize that claim to mean that mass itself "redshifts" in changes to the Schwarzschild M parameter.
3) You then further generalize that claim to mean that the redshift in the global measure of mass (Bondi) and the global mass parameter of the spacetime can be localized to the mass that is added to the system, and therefore an additional mass m is "redshifted" wrt local interactions.
4) You then further generalize that since local interactions are unchanged charge must also be redshifted.
5) You then note that no charge is radiated to null infinity. Therefore, since charge is redshifted and not radiated away it must not be conserved.

Is that an accurate representation of your line of reasoning?

 

[Dale]

In fact apart from that added thought in #248 nothing substantially new has been added since #1 really. So I don't know, in the end it may simply come down to another fizzle/fadeout which at bottom amounts to "concensus/majority opinion ruulz - OK!" But no - sour grapes premature at this point.

Q-reeus, from #1 you have never even rigorously defined let alone justified your key "mass redshifts" concept. This has nothing to do with intellectual "mob rule" but instead, a lack of rigor in your idea. You are absolutely convinced by your handwaving arguments that there is yet another flaw in GR, but when pushed to clarify your key concepts you cannot do so.

 

[GAsahi]

Easy, virtual photons are off-shell, meaning they can travel faster than c and even have mass.

True. How does this "help" in propagating past the EH? For example, having "mass" seems more like hindrance, not help.

 

[Dale]

How does this "help" in propagating past the EH?

There are no lightlike nor timelike paths from inside the EH to outside, but there are spacelike paths. So something which can travel faster than c, like a virtual photon, can travel along such spacelike paths from inside to outside.

 

[GAsahi]

There are no lightlike nor timelike paths from inside the EH to outside, but there are spacelike paths. So something which can travel faster than c, like a virtual photon, can travel along such spacelike paths from inside to outside.

Thank you.

 

[Q-reeus]

GAsahi: "How would the electro(static) field propagate past the EH? Photons don't, how would virtual photons (the carriers of em field) ?"
Easy, virtual photons are off-shell, meaning they can travel faster than c and even have mass.

Easy to say. But having accused me of much hand-waving argument, is that bit anything other than very hand-wavy? This thread began as a fork off from another one that was QED based. Some points were raised there along your line and I raised a (admittedly somewhat 'hand-wavy') counterpoint that never did get responding to: https://www.physicsforums.com/showpost.php?p=3943187&postcount=11
[for the record, I here withdraw the remarks made there about 'immunity to redshift' made in 3rd para there - which was done in haste and counter to my own previous arguments on that issue. Did'nt withdraw back then then owing to possible admin censure over a perceived 'bumping a thread twice' rule]

 

[Dale]

Easy to say. But having accused me of much hand-waving argument, is that bit anything other than very hand-wavy?

Agreed. I personally prefer to stick with classical mechanics rather than quantum mechanics for that reason.

The best that I can do is to show rigorously that there are spacelike geodesics from inside to outside. I cannot rigorously determine how many virtual photons would be exchanged along any given such path. That would prove that virtual photon exchange could occur, but not prove anything about the strength of the exchange. Are you interested in that?

 

[Q-reeus]

So, let me see if I correctly understand your chain of reasoning.

1) There exist three global measures of mass that could be considered in an asymptotically flat and static metric. Out of those three you equate the Bondi mass with the M parameter of the Schwarzschild metric.
2) You note that the Bondi mass "redshifts" in the specific case where energy is radiated to null infinity. You then generalize that claim to mean that mass itself "redshifts" in changes to the Schwarzschild M parameter.
3) You then further generalize that claim to mean that the redshift in the global measure of mass (Bondi) and the global mass parameter of the spacetime can be localized to the mass that is added to the system, and therefore an additional mass m is "redshifted" wrt local interactions.
4) You then further generalize that since local interactions are unchanged charge must also be redshifted.
5) You then note that no charge is radiated to null infinity. Therefore, since charge is redshifted and not radiated away it must not be conserved.

Is that an accurate representation of your line of reasoning?

Oh dear, I detect a certain tone here - leading up to your #279. My answer then begins with a little truism. One says the glass is half-empty. Another says it's half-full. Both are correct but note the difference in emphasis and outlook. Politicians and lawyers are masters of this art and can have a mob ready to lynch or cheer, convict or acquit, all based on the same available evidence. Repeated sequential use of a term like 'further generalize' seems in keeping with that style. But I should not prejudge your intent, so now to a point-by-point response:

1) Had never thought of it as 'out of three' until PeterDonis made that distinction in #260. Owing to the way the distinctions are arrived at there, it would be insane to choose other than Bondi given what we are looking at in the current scenario.
2) Correct and obviously correct. Do you find differently? On what basis if so? Recall in this type of thing we start with n atoms 'at infinity' (or at least as a static distribution 'further out' than later) and after assembly as a stable, static gravitating mass distribution there are still n atoms. We are concerned with the gravitating mass owing to those n atoms - not (n atoms + loss of PE radiated to infinity)! Does gravitating mass before = gravitating mass after by your own reckoning? So divide total by n and what do we have on a before/after per-atom basis? Same thing applies to EM energy of charge distributions btw. And how could it be otherwise - atoms after all have a significant internal EM energy contribution to total mass.
3) Basically yes and I refer you to my position in 2) above and as then logically followed through back in #51 this thread (and same argument made in previous threads).
4) Note good and well how I now see in #248 the consistent approach that yields that as so 'in effect'.
5) I made a clear point of distinction between *effective* charge invariance violation, and conservation of charge, back in #25.

Where to now? I shudder to think.

 

[Q-reeus]

Q-reeus, from #1 you have never even rigorously defined let alone justified your key "mass redshifts" concept. This has nothing to do with intellectual "mob rule" but instead, a lack of rigor in your idea. You are absolutely convinced by your handwaving arguments that there is yet another flaw in GR, but when pushed to clarify your key concepts you cannot do so.

And if I was in an apparently similar uncharitable and pugnacious frame of mind, I would characterize my opposition here of being narrow-minded 'defenders of the faith' with an unwavering quasi-religious committment to the status-quo. I would be basing that on the fact that such opponents have deftly avoided answering, among other matters, one in particular rather simple bottom-line point raised yet again in #272:

Energy of any kind but particularly here electrostatic field energy, at rest in a gravitational potential (dipole, internal atomic EM fields etc.), is by any reasonable definition, depressed wrt the non-gravitational case. How is this consistently reconciled with the logically necessary RN metric requirement that field strength can suffer no gravitational reduction? Still waiting for that answer (#254 etc).

 

[PeterDonis]

How would the electro(static) field propagate past the EH? Photons don't, how would virtual photons (the carriers of em field) ?

The field doesn't have to propagate from inside the EH to outside. The EM field outside the hole that makes charged particles move differently from uncharged ones is not coming from inside the hole; it's coming from the charge-current density of the object that originally collapsed to form the hole. Similarly, the gravity felt outside the hole isn't coming from inside the hole; it's coming from the stress-energy of the object that originally collapsed to form the hole.

This has come up previously in this thread. See this post:

https://www.physicsforums.com/showpost.php?p=3965429&postcount=264

and the one it links to.

 

[GAsahi]

The field doesn't have to propagate from inside the EH to outside. The EM field outside the hole that makes charged particles move differently from uncharged ones is not coming from inside the hole; it's coming from the charge-current density of the object that originally collapsed to form the hole. Similarly, the gravity felt outside the hole isn't coming from inside the hole; it's coming from the stress-energy of the object that originally collapsed to form the hole.

This has come up previously in this thread. See this post:

https://www.physicsforums.com/showpost.php?p=3965429&postcount=264

and the one it links to.

Thank you, this makes perfect sense, I should have thought about the fact that the formation of the BH plays a a key role, the field was present prior to the BH formation. Thank you for your excellent answer.

 

[Dale]

1) Had never thought of it as 'out of three' until PeterDonis made that distinction in #260. Owing to the way the distinctions are arrived at there, it would be insane to choose other than Bondi given what we are looking at in the current scenario.

I have no problem with choosing Bondi, just with equating it to the Schwarzschild M parameter. I cannot find any indication that the Schwarzschild mass parameter refers to the Bondi mass.

2) Correct and obviously correct. Do you find differently? On what basis if so?

Yes. On the basis that I don't see the connection between the Bondi mass and the Schwarzschild mass parameter.

3) Basically yes and I refer you to my position in 2) above and as then logically followed through back in #51 this thread (and same argument made in previous threads).

I am actually not sure about this one. This is what I am working on the math for. In order to localize a mass "redshift" you clearly need a local definition rather than the Bondi definition which is a global mass and cannot be localized. I gave a suggested definition for the redshift of a localized quantity based on parallel transport, and am working through that definition.

4) Note good and well how I now see in #248 the consistent approach that yields that as so 'in effect'.
5) I made a clear point of distinction between *effective* charge invariance violation, and conservation of charge, back in #25.

I think 4 and 5 are solid.

 

[PeterDonis]

And if I was in an apparently similar uncharitable and pugnacious frame of mind, I would characterize my opposition here of being narrow-minded 'defenders of the faith' with an unwavering quasi-religious committment to the status-quo.

Q-reeus, one big difference between you and those of us who have been disagreeing with you, IMO, is that you put a lot more faith in your intuition than we do. You come up with an intuitive line of reasoning, and you trust it to give you a reasonably accurate picture of the physics. We don't. We (or at least I, I can't speak for others here) may use intuitive arguments to get started, but I view those arguments as suggestions about where to look in the actual physics; I don't view them as telling me the actual physics. To find the actual physics, you have to look at the math.

Take the example you bring up right after the above quote:

Energy of any kind but particularly here electrostatic field energy, at rest in a gravitational potential (dipole, internal atomic EM fields etc.), is by any reasonable definition, depressed wrt the non-gravitational case.

This is not what the math says. The math says that if you *transmit* energy from one place to another in a curved spacetime, local observers at the second place may measure a change relative to local observers in the first place, depending on how the contraction of the 4-momentum being transmitted with the 4-velocity of the observers changes. The math does not say that "energy is depressed"; that's your intuitive interpretation, which you appear to have arrived at without even looking at the math.

How is this consistently reconciled with the logically necessary RN metric requirement that field strength can suffer no gravitational reduction?

Again, the math does not say that "field strength suffers no gravitational reduction". It says what I said above, about energy being "transmitted", applied to the energy stored in a dipole, and that's all. The part about "field strength being reduced" is, once again, your intuitive interpretation. There's nothing in the math that says "field strength is reduced". In fact, I'm not even sure what mathematical object would correspond to "field strength" in your dipole scenario.

So when you find me objecting to your intuitive arguments, it's because I can't see a way to relate them to the math. And without that, I don't trust them. I recognize that the concepts you are using have intuitive force, and so I am willing to spend time examining how those concepts work and whether there might be some parallel in the math. But if I can't find a parallel in the math, then my conclusion is that the intuitive arguments simply aren't valid.

One final point: why all this emphasis on the math? Because that's what generates the detailed predictions that actually get compared with experiment. That's what justifies our belief that GR is correct within its domain of validity. The intuitive arguments don't play any role in that at all.

 

[PeterDonis]

I have no problem with choosing Bondi, just with equating it to the Schwarzschild M parameter. I cannot find any indication that the Schwarzschild mass parameter refers to the Bondi mass.

Strictly speaking, a Schwarzschild BH cannot radiate anything away to infinity, so its ADM mass and Bondi mass are the same, and are equal to the M that appears in the metric. For an exact Schwarzschild BH, that's an exact mathematical result. (I believe there is also an exact result for the Komar mass being equal to M.)

In the scenario we're considering, where something falls into a BH and some energy gets radiated away to infinity, we're not talking about an exact solution to the EFE any more, but an approximate solution where we have to patch together at least three regions: an initial region with a BH and a massive object "hovering" at rest outside it; a transition region where the object is lowered into the BH and some energy gets radiated away to infinity; and a final region with a larger BH.

Based on how the ADM mass and Bondi mass work (the former takes the limit as you go to spacelike infinity, the latter as you go to future null infinity), I would expect that for the above approximate solution, the ADM mass will include the energy that gets radiated away and the Bondi mass will not. If there is nothing else present in the spacetime, the Bondi mass will then equal the M parameter of the BH after the process is complete.

 

[Dale]

Strictly speaking, a Schwarzschild BH cannot radiate anything away to infinity, so its ADM mass and Bondi mass are the same, and are equal to the M that appears in the metric. For an exact Schwarzschild BH, that's an exact mathematical result. (I believe there is also an exact result for the Komar mass being equal to M.).

Do you have anything that shows that, or any reference?

I think that we can use Birkhoff's theorem to extend the Schwarzschild M to dynamic cases where spherical symmetry and asymptotic flatness are maintained. Suppose there is a planet which is suddenly converted to an incoherent spherical flash of light (e.g. antimatter anhilation). At that point, any region outside of the light cone will still have a Schwarzschild spacetime with the original M, but, if I understand Bondi correctly, the Bondi mass will already be 0. So I am very sceptical about the Bondi mass being equal to the Schwarzschild mass parameter in cases, like this one, where it disagrees with the other masses.

 

[Q-reeus]

I have no problem with choosing Bondi, just with equating it to the Schwarzschild M parameter. I cannot find any indication that the Schwarzschild mass parameter refers to the Bondi mass...
Q-reeus: "2) Correct and obviously correct. Do you find differently? On what basis if so?"
Yes. On the basis that I don't see the connection between the Bondi mass and the Schwarzschild mass parameter.

Recall definitions in #260 have that only Bondi mass subtracts energy radiated away during assembly from less to more dense state (and note that final state need not at all be a BH). Why on Earth would one want to include that energy radiated to infinity when determining the gravitating mass (Schwarzscild mass parameter M)? Or is my silly intuition befuddling my mind again?

I am actually not sure about this one. This is what I am working on the math for. In order to localize a mass "redshift" you clearly need a local definition rather than the Bondi definition which is a global mass and cannot be localized. I gave a suggested definition for the redshift of a localized quantity based on parallel transport, and am working through that definition.

Keep at it then, but remember 'the math' has to have logical underpinnings, in particular as it is applied to physics. For the latter there is always a model to be worked from. Some apparently think that 'the math' is an absolute thing standing god-like above all else and needing no scrutiny based on logic/'intuition'.

I think 4 and 5 are solid.

I cling to hope.

 

[Q-reeus]

Q-reeus, one big difference between you and those of us who have been disagreeing with you, IMO, is that you put a lot more faith in your intuition than we do. You come up with an intuitive line of reasoning, and you trust it to give you a reasonably accurate picture of the physics. We don't. We (or at least I, I can't speak for others here) may use intuitive arguments to get started, but I view those arguments as suggestions about where to look in the actual physics; I don't view them as telling me the actual physics. To find the actual physics, you have to look at the math.

Not saying you necessarily are undermining me by always referring to any argument I raise as 'intuition', but think about substituting the word 'logic' or 'logical' instead, at least on occasion.

Q-reeus: "Energy of any kind but particularly here electrostatic field energy, at rest in a gravitational potential (dipole, internal atomic EM fields etc.), is by any reasonable definition, depressed wrt the non-gravitational case."

This is not what the math says. The math says that if you *transmit* energy from one place to another in a curved spacetime, local observers at the second place may measure a change relative to local observers in the first place, depending on how the contraction of the 4-momentum being transmitted with the 4-velocity of the observers changes. The math does not say that "energy is depressed"; that's your intuitive interpretation, which you appear to have arrived at without even looking at the math.

As per comments in previous thread to DaleSpam, math MUST have logical underpinnings. If the basic logic/philosophy is screwy, one has GIGO (Garbage-In/Garbage-Out), no matter how sophisticated that is mathematically expressed. Apply then the same 'transmission' approach to field itself. The field 'transmitted' from one place to another suffers zero reduction, regardless of gravitational potential difference, if RN is true. Do you dispute my intuition/logic on that? So 'intuitively' follow that through as I have done ad nauseam here. Show how to reconcile with what I said 'intuitively' in #272.

And here's a test case: There is a distant star. Also a distant static charge either directly behind or in front of said star wrt our line-of-sight. A massive BH sweeps across our line-of-sight, between us and star/charge. Gravitational lensing uncontroversially distorts the starlight received. What does your 'math' tell you about the field lines of that charge - will they distort or not? You already know my opinion on that one - but I'm asking for yours.

Again, the math does not say that "field strength suffers no gravitational reduction". It says what I said above, about energy being "transmitted", applied to the energy stored in a dipole, and that's all. The part about "field strength being reduced" is, once again, your intuitive interpretation. There's nothing in the math that says "field strength is reduced". In fact, I'm not even sure what mathematical object would correspond to "field strength" in your dipole scenario.

You mean GR cannot give us a value for say dipole field strength as function of r,theta, phi, - with and then without a mass M present? How very sad!

So when you find me objecting to your intuitive arguments, it's because I can't see a way to relate them to the math. And without that, I don't trust them. I recognize that the concepts you are using have intuitive force, and so I am willing to spend time examining how those concepts work and whether there might be some parallel in the math. But if I can't find a parallel in the math, then my conclusion is that the intuitive arguments simply aren't valid.

Again, please consider the possibility that intuition = logic, at least sometimes.

One final point: why all this emphasis on the math? Because that's what generates the detailed predictions that actually get compared with experiment. That's what justifies our belief that GR is correct within its domain of validity. The intuitive arguments don't play any role in that at all.

There is absolutely no experimental/observational support for a RN BH. If there were I would opt for us all being in some kind of computer simulated universe.

 

[PeterDonis]

Do you have anything that shows that, or any reference?

I don't have the textbooks handy to check exact page references, but I'm pretty sure it's discussed in both MTW and Wald. I don't know that they give the complete proof.

Actually, given the formula I posted in #262, deriving the result should be pretty straightforward. I'll put that in a separate post.

I think that we can use Birkhoff's theorem to extend the Schwarzschild M to dynamic cases where spherical symmetry and asymptotic flatness are maintained.

For cases where the spacetime is vacuum for all time outside some finite radius r, yes, I agree. But for cases where radiation escapes to infinity, I'm not sure it would work.

Suppose there is a planet which is suddenly converted to an incoherent spherical flash of light (e.g. antimatter anhilation). At that point, any region outside of the light cone will still have a Schwarzschild spacetime with the original M, but, if I understand Bondi correctly, the Bondi mass will already be 0.

I agree the Bondi mass will be 0, but I'm not sure about the "already". On thinking it over, I think I wasn't clear about how the Bondi mass works. A given spacetime has only one future null infinity, even if we model the spacetime by patching together regions built from different solutions of the EFE. So the Bondi mass would not "change" as things happen; it would only have one value which reflect the end result of all the changes. So in this case the Bondi mass would just be 0; it wouldn't change from M to 0. The effect of the change would be reflected in the difference between the ADM mass, which would be M (because the radiation escapes to future null infinity, not spacelike infinity), and the Bondi mass of 0 (which could be thought of as the "M" of the region inside the shell of radiation). Similarly, in the case we've been discussing where a mass is lowered into a BH and radiation escapes to infinity, the Bondi mass would always be the final mass of the BH, and the ADM mass would always include the energy of the radiation. So I misstated things somewhat before for these examples.

So I am very sceptical about the Bondi mass being equal to the Schwarzschild mass parameter in cases, like this one, where it disagrees with the other masses.

See above. In cases where we have two effective "M" parameters, the ADM mass will equal one and the Bondi mass will equal the other.

 

[Dale]

Keep at it then, but remember 'the math' has to have logical underpinnings,

I would say it the other way. Logic has to have mathematical underpinnings.

However, in this case I think it isn't so much a matter of logic as a matter of definition. I have suggested a definition of what it means for some local quantity to "redshift" and I am pursuing the application of that definition to various quantities. However, other definitions could be proposed with conflicting conclusions. I encourage you to think of how you would rigorously define "redshift" of a local quantity.

 

[stevendaryl]

Not saying you necessarily are undermining me by always referring to any argument I raise as 'intuition', but think about substituting the word 'logic' or 'logical' instead, at least on occasion.

The word "logic" is not appropriate for your type of argument. The point about logic is that it carefully exposes what assumptions are being made and what conclusions definitely follow from those assumptions. You're not doing that at all. The sort of reasoning that you're doing is intuitive, but it's NOT logical, in the sense of being deductive.

 

[Q-reeus]

However, in this case I think it isn't so much a matter of logic as a matter of definition. I have suggested a definition of what it means for some local quantity to "redshift" and I am pursuing the application of that definition to various quantities. However, other definitions could be proposed with conflicting conclusions. I encourage you to think of how you would rigorously define "redshift" of a local quantity.

Not sure what you mean here. The very term 'redshift' normally implies nonlocal connection. If there is anywhere at all in any entry I have made here that seems to confuse that notion please refer to it and I will endeavour to make amends post-haste!

 

[Q-reeus]

The word "logic" is not appropriate for your type of argument. The point about logic is that it carefully exposes what assumptions are being made and what conclusions definitely follow from those assumptions. You're not doing that at all. The sort of reasoning that you're doing is intuitive, but it's NOT logical, in the sense of being deductive.

I respect that you believe this, but also respectfully disagree. if you want to re-engage me in specifics I might consider things on a case-by-case basis, but not polemic.

 

[Dale]

Why on Earth would one want to include that energy radiated to infinity when determining the gravitating mass (Schwarzscild mass parameter M)? Or is my silly intuition befuddling my mind again?

Because it still gravitates before it radiates away. I.e. if you have a test object outside a spherically symmetric null dust (a shell of photons) then that test object will orbit and experience tidal forces until the null dust expands past its radius, despite the fact that the Bondi mass is 0 even before it radiates away.