Is 'charged black hole' an oxymoron?

[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.