Is 'charged black hole' an oxymoron?

[Dale]

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!

Yes, every time that you have attributed the redshift to a specific object, stating that it is redshifted in its interactions locally with other objects. That is, in fact, the key point of your argument as I understand it (points 3 and 4 above).

If that is not what you intend, then I would once again encourage you to rigorously define what you mean for a localized mass or charge to "redshift". Otherwise I will continue with the parallel transport on null geodesics definition. My problem is that you say "the very term 'redshift' normally implies ..." without a solid definition of redshift that can be used to derive that implication.

 

[Dale]

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.

If Birkhoff's theorem doesn't apply to solutions where energy goes to infinity then I think we really cannot use the Bondi mass as the Schwarzschild mass in any situation where it differs from the other masses. In such situations there simply is no Schwarzschild mass since the spacetime is not static and it cannot be related to the Schwarzschild spacetime via Birkhoff's theorem.

So I simply don't see any way that the Bondi mass can be equated with the Schwarzschild mass when Bondi differs from ADM.

 

[PeterDonis]

If Birkhoff's theorem doesn't apply to solutions where energy goes to infinity then I think we really cannot use the Bondi mass as the Schwarzschild mass in any situation where it differs from the other masses. In such situations there simply is no Schwarzschild mass since the spacetime is not static and it cannot be related to the Schwarzschild spacetime via Birkhoff's theorem.

You raise a good point--in looking up references for the Bondi mass, I see various sources saying that it does not include the energy contained in *gravitational* radiation that goes to infinity, but I have not seen a statement about other types of radiation. The key difference, of course, is that the presence of gravitational radiation only allows the spacetime exterior to the central object to still be vacuum (zero stress-energy tensor); other types of radiation require a nonzero SET in the exterior region. So I'm not sure now exactly how the Bondi mass would handle such cases; I think it would still not include the energy radiated to infinity, but I am not positive.

However, even gravitational radiation requires a non-spherically symmetric spacetime, so even in that case Birkhoff's Theorem would not apply. So I think the general statement that Birkhoff's Theorem does not apply in any spacetime where "energy goes to infinity" is true. And I think I agree that in such cases, the "Schwarzschild mass" as it stands is not well-defined; you have to specify whether you are talking about a parameter in the metric, or the result of one of the integrals such as the ADM, Bondi, or Komar integral, since they can all differ in principle.

 

[PeterDonis]

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.

Others have already commented on this, but I would point out that "logic" requires axioms to start with, and requires a consistent set of propositions to be built up from those axioms. What I'm calling "math" is really a large set of such propositions built up from axioms, whose consistency has been carefully checked. But to carefully check that, you have to have an unambiguous way of expressing propositions, and an unambiguous way of expressing the logical connections between them. "Intuition" doesn't have any of that; it has propositions and logical connections expressed in English, which is not unambiguous, as I've pointed out before, and it certainly doesn't have a large consistent set of propositions whose consistency has been carefully checked.

As it happens, you go right on to give a good example:

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.

What does this mean, precisely? What is the "field transmitted from place to place"? What does "suffers zero reduction" mean? Try giving these things precise meanings, before asking us to accept your "intuition" about them. By "precise meanings" I mean actual observables. I've already described several such, and shown how they are all consistent.

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.

I already know your opinion? This test case is very different from what we have been discussing; what's the connection? Your "intuition" tells you they are connected? Can you give anything more precise than that? And what observable corresponds to the "field lines" of the charge?

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?

GR can tell you what the EM field tensor is due to the dipole. Is that what you mean by "dipole field strength"? Or it can tell you what the contraction of the EM field tensor is with some 4-vector. Is that what you mean by "dipole field strength"? Or do you mean something else?

Specify a precise observable, and GR will tell you how to calculate it. But GR can't promise to give a precise meaning to all your imprecise intuitive terms. That's part of what I meant when I say that others of us rely on intuition a lot less than you do. You are trying to reason directly with your intuitive terms. We are starting with the fundamentals, the math, using that to compute an answer, and then some people, like me, are willing to try and see how that answer might be described using your intuitive terms. There might be no way to do that that satisfies your intuition; but you view that as a problem with GR, and we view that as a problem with your intuition.

There is absolutely no experimental/observational support for a RN BH.

This is true. However, there is lots of experimental support for (1) the EFE as applied to spherically symmetric spacetimes; (2) the EM field tensor and the covariant form of Maxwell's equations as applied to electrodynamics under all conditions we have tested. R-N geometry is simply the result of combining the two.

Also, as has been said before, we can just as well consider the R-N geometry exterior to a charged massive object, rather than a BH. That involves only the R-N region exterior to the horizon, which avoids issues with what goes on inside the horizon, and is therefore an unproblematic solution of the EFE combined with Maxwell's equations.

 

[Q-reeus]

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.

Well no controversy here then. In every posting of mine where a process of mass/energy/charge 'redshift' has occurred, it's always assumed - as in the typical 'winching down' examples, net loss of system energy is just that. We discard that which the winch has received - it's now exterior to the system of interest. Same with heat radiated away etc. Thought there was no room for confusion over that. The only real issue I see we are having is in the matter of whether the net system reduction should be regarded as diffused throughout or localized. And that has been discussed already at some length. As discussed next posting - that's really a moot thing.

 

[Q-reeus]

Yes, every time that you have attributed the redshift to a specific object, stating that it is redshifted in its interactions locally with other objects. That is, in fact, the key point of your argument as I understand it (points 3 and 4 above).

If that is not what you intend, then I would once again encourage you to rigorously define what you mean for a localized mass or charge to "redshift". Otherwise I will continue with the parallel transport on null geodesics definition.

You are referring to 3) and 4) back in #278 no doubt. We have discusssed that and you gave a verdict already in #289. Was about to refer to a previous entry but you dislike that so here goes again.

*All* matter/energy at rest in the potential well of a large gravitating mass M adds a reduced gravitating mass m' to M according to m' = m(1-2GM/(rc2)), where m<<M (Are we now clear that the lost 'assembly' PE has been radiated far, far away?). So the example(s) I gave much earlier of say drawing two small test charges transversely apart to form a dipole will require less energy than with M absent - by that (1-2GM/(rc2)) factor. Requiring I refer to which mass is 'really' locally redshifted is spurious in that all matter at that potential is. However if one lowers mass down a rope and then annihilates it as radiation escaping back to infinity, there is properly a sense that the redshift was 'localized' since just those atoms disappeared, to be replaced with redshifted radiation. And need I repeat - the balance was already previously transferred out to the hoisting down process.

NOW FOLLOW THIS BIT THROUGH CAREFULLY. MY 'INTUITION' IS THAT THE VERY EXISTENCE OF A RN BH IMPLIES GRAVITATIONAL POTENTIAL (READ REDSHIFT FACTOR (1-2GM/(rc2))) CANNOT ALLOW ANY CHANGE IN FIELD STRENGTH - OR FIELD DIRECTION/PATTERN, FOR SUCH DIPOLE OR INDEED ANY CHARGE DISTRIBUTION. THIS MUST *LOGICALLY* EXTEND TO INTERACTION OF CHARGE WITH ANY GRAVITATING MASS. FOLLOW THAT LOGIC/'INTUITION' THROUGH. IT MEANS ANY AND EVERY CHARGE IS A MIRACULOUS BEACON OF FLAT SPACETIME - IT CANNOT BE EFFECTED IN ANY WAY BY SAY THE CLOSE PROXIMITY OF A MASSIVE BH (ASSUMING OF COURSE STATIC SEPARATION IS SOMEHOW MAINTAINED). A REDICULOUS TO ME CONCLUSION BUT ONE THAT INEVITABLY FOLLOWS IF RN BH CAN EXIST. THINK ABOUT IT.

And if PeterDonis gets around to answering my little personal challenge on that issue in #294 (nicely boldfaced just to make sure it didn't get missed somehow), the penny might drop. Sometimes 'intuition' can be a helpful thing. And if I'm wrong, an explanation covering that and other related consequences should not be hard to come by. Qualitative or quantitative. I retire exhausted!

 

[PeterDonis]

And if PeterDonis gets around to answering my little personal challenge on that issue in #294 (nicely boldfaced just to make sure it didn't get missed somehow)

I didn't miss it, as my last post should make clear. But I can't even try to answer it until you define more precisely what you mean by "what happens to the field lines". The gravitational lensing has an unambiguous observable: the direction from which the light comes to my detector changes when the lensing object is in the path. What is the unambiguous observable that tells me whether or not something has happened to the field lines?

 

[Dale]

*All* matter/energy at rest in the potential well of a large gravitating mass M adds a reduced gravitating mass m' to M according to m' = m(1-2GM/(rc2)), where m<<M

This is not true in *all* cases. It is only true in cases where a quantity of energy exactly equal to (m-m')c^2 is extracted from the system. There are many ways to add an additional mass that do not involve radiating this quantity of energy away.

In those situations where the energy was radiated away it seems strange to call that process "redshift", but regardless of what you call it, it seems more like a statement about energy flux across a surface than about any gravitational effect.

So the example(s) I gave much earlier of say drawing two small test charges transversely apart to form a dipole will require less energy than with M absent - by that (1-2GM/(rc2)) factor.

How do you conclude this? The change in the global mass, whether Schwarzschild M, Bondi, ADM, or Komar, tells you nothing about a local interaction like this. I actually think that you can make a case for this concept using parallel transport, but I would encourage you to think about this rigorously.

Requiring I refer to which mass is 'really' locally redshifted is spurious in that all matter at that potential is.

Not true.

However if one lowers mass down a rope and then annihilates it as radiation escaping back to infinity, there is properly a sense that the redshift was 'localized' since just those atoms disappeared, to be replaced with redshifted radiation.

I agree. Again, this concept is related to parallel transport.

NOW FOLLOW THIS BIT THROUGH CAREFULLY. MY 'INTUITION' IS THAT THE VERY EXISTENCE OF A RN BH IMPLIES GRAVITATIONAL POTENTIAL (READ REDSHIFT FACTOR (1-2GM/(rc2))) CANNOT ALLOW ANY CHANGE IN FIELD STRENGTH - OR FIELD DIRECTION/PATTERN, FOR SUCH DIPOLE OR INDEED ANY CHARGE DISTRIBUTION. THIS MUST *LOGICALLY* EXTEND TO INTERACTION OF CHARGE WITH ANY GRAVITATING MASS. FOLLOW THAT LOGIC/'INTUITION' THROUGH. IT MEANS ANY AND EVERY CHARGE IS A MIRACULOUS BEACON OF FLAT SPACETIME - IT CANNOT BE EFFECTED IN ANY WAY BY SAY THE CLOSE PROXIMITY OF A MASSIVE BH (ASSUMING OF COURSE STATIC SEPARATION IS SOMEHOW MAINTAINED). A REDICULOUS TO ME CONCLUSION BUT ONE THAT INEVITABLY FOLLOWS IF RN BH CAN EXIST. THINK ABOUT IT.

I agree that the conclusion is ridiculous.

 

[Dale]

Well no controversy here then. In every posting of mine where a process of mass/energy/charge 'redshift' has occurred, it's always assumed - as in the typical 'winching down' examples, net loss of system energy is just that. We discard that which the winch has received - it's now exterior to the system of interest.

Which makes your redshift concept a statement about net energy flux rather than gravitation.

 

[Austin0]

Originally Posted by Austin0

If a mass is transported to a lower altitude it then requires more energy to maintain a state of rest wrt the gravitating body .

It doesn't require any energy to maintain a state of rest wrt the gravitating body. E.g. consider a book on a table.

Is that actually the case?

The book creates deformation stresses on the table. The table necessarily counters this force through electrostatic and nuclear forces (Van der Walls etc). This is a continuing condition so implies a continuing flow of energy.
How to analyze this in terms of energy conservation is beyond me as the electrostatic and nuclear forces seem to be effectively inexhaustible but it seems that there has to be energy in play. Just as simply standing in gravity requires additional energy.
We consider that the table surface is accelerating upward even though there is n o coordinate displacement. Doesn't acceleration imply force/energy?
SO comparably shouldn't we view the book as having inertial momentum downward , exerting force on the table , even though in this case also there is no coordinate motion??

 

[Dale]

The book creates deformation stresses on the table. The table necessarily counters this force through electrostatic and nuclear forces (Van der Walls etc). This is a continuing condition so implies a continuing flow of energy.

This is an incorrect understanding of energy. Once the small deformation is done there is no motion, so no work is being done. Energy does not need to continually flow in order to provide a static force.

 

[Austin0]

This is an incorrect understanding of energy. Once the small deformation is done there is no motion, so no work is being done. Energy does not need to continually flow in order to provide a static force.

Oh i certainly understand the normal view of energy you are presenting here , having thought exactly the same until encountering this situation .
So if there can be acceleration without motion perhaps it is possible to have energy expenditure without action. At this point I am just looking at the situation from all sides without any conclusions. In the end I may end up right where I started, agreeing with your view.

So are you saying that the book ceases to exert downward force on the table once the initial adjustment is made?
If so i would say my rear contact with my chair seat disagrees with you.

If the book is hovering under thrust at an equivalent height this would necessitate continuing energy of acceleration.This also implies that the book is effecting an equivalent continuing counter force ( momentum?). yes?
The EP would seem to suggest, as the book's force is the same in both cases, the upward acceleration/force would be equivalent .Isn't this the basis of the EP ? An accelerometer doesn't measure the downward force but rather the upward force acting against the inertia of some internal mass of the instrument?
Maybe it is my understanding of the EP that is lacking? ;-(

 

[TrickyDicky]

This is an incorrect understanding of energy. Once the small deformation is done there is no motion, so no work is being done. Energy does not need to continually flow in order to provide a static force.

This would be correct only if the table is considered an inertial object (as it is done in most practical physics exercises, there is a lab frame considered to be at rest,it is an idealization that works great for most practical problems), but we know that is not the case in reality, the table is non-inertial and in continuous motion so there is work done. An accelerometer in the surface of the Earth measures proper acceleration.

 

[TrickyDicky]

Oh i certainly understand the normal view of energy you are presenting here , having thought exactly the same until encountering this situation .
So if there can be acceleration without motion perhaps it is possible to have energy expenditure without action. At this point I am just looking at the situation from all sides without any conclusions. In the end I may end up right where I started, agreeing with your view.

So are you saying that the book ceases to exert downward force on the table once the initial adjustment is made?
If so i would say my rear contact with my chair seat disagrees with you.

If the book is hovering under thrust at an equivalent height this would necessitate continuing energy of acceleration.This also implies that the book is effecting an equivalent continuing counter force ( momentum?). yes?
The EP would seem to suggest, as the book's force is the same in both cases, the upward acceleration/force would be equivalent .Isn't this the basis of the EP ? An accelerometer doesn't measure the downward force but rather the upward force acting against the inertia of some internal mass of the instrument?
Maybe it is my understanding of the EP that is lacking? ;-(

Your rear is entitled to disagree.

 

[Dale]

So are you saying that the book ceases to exert downward force on the table once the initial adjustment is made?

No, I am most definitely not saying that. I explicitly said "Energy does not need to continually flow in order to provide a static force." I.e. there is a continued force, it does not require energy.

If the book is hovering under thrust at an equivalent height this would necessitate continuing energy of acceleration.This also implies that the book is effecting an equivalent continuing counter force ( momentum?). yes?
The EP would seem to suggest, as the book's force is the same in both cases, the upward acceleration/force would be equivalent .

In the thrust example the KE of the exhaust is being increased (a lot), therefore energy is being used. None of that energy is going into the book whose KE and PE are remaining constant.

Isn't this the basis of the EP ? An accelerometer doesn't measure the downward force but rather the upward force acting against the inertia of some internal mass of the instrument?
Maybe it is my understanding of the EP that is lacking? ;-(

Probably it is more a misunderstanding of physics in non-inertial frames. Please see my response to Tricky Dicky below.

 

[Dale]

This would be correct only if the table is considered an inertial object (as it is done in most practical physics exercises, there is a lab frame considered to be at rest,it is an idealization that works great for most practical problems), but we know that is not the case in reality, the table is non-inertial and in continuous motion so there is work done. An accelerometer in the surface of the Earth measures proper acceleration.

No, I am not considering the table an inertial object, if the table were inertial then the force on the book would be 0.

You misunderstand how energy works in a non-inertial frame. In a non-inertial frame, like the usual frame attached to the surface of the earth, there is a fictitious force. The fictitious force, in this case, is equal to mg and directed downwards. We know that there is a fictitious force on the book precisely because an accelerometer measures a proper acceleration of g directed upwards and yet the book is not accelerating relative to our frame.

Now, work is f.d, so as an object is moved upwards against this fictitious force it requires an amount of work equal to f.d=mgh. Conversely, as an object is lowered the fictitious force does an amount of work equal to mgh. So, the ficitious force has an associated potential energy. (remember, energy is frame variant)

So, the book, sitting on the table at rest, has no change in KE. It also has no change in PE. No work is being done on it. There is no change to its internal structure or temperature nor anything else where energy could go. There is no change in any energy associated with the book. Despite the fact that there is a force on the book (two forces actually) and the book measures a proper acceleration and is therefore non-inertial.

 

[TrickyDicky]

You misunderstand how energy works in a non-inertial frame. In a non-inertial frame, like the usual frame attached to the surface of the earth, there is a fictitious force. The fictitious force, in this case, is equal to mg and directed downwards. We know that there is a fictitious force on the book precisely because an accelerometer measures a proper acceleration of g directed upwards and yet the book is not accelerating relative to our frame.

(remember, energy is frame variant)

Not exactly, KE is frame dependent, energy is a conserved quantity in Newtonian mechanics (I understand you are restricting this to the Newtonian mechanics POV since you were talking about fictitious forces).

So, the book, sitting on the table at rest, has no change in KE. It also has no change in PE. No work is being done on it. There is no change to its internal structure or temperature nor anything else where energy could go. There is no change in any energy associated with the book. Despite the fact that there is a force on the book (two forces actually) and the book measures a proper acceleration and is therefore non-inertial.

You are forgetting here that work, like KE is a frame dependent quantity. I know the example of the book and the table is considered to have 0 net moment, with net moment defined as change in KE, that is not what I referred to when I said work was being done.
The conventional Newtonian treatment with fictitious forces is fine, I have nothing against it as long as one understands its range of validity.
I was pointing to a more realistic treatment, more like GR's Schwarzschild solution (so energy is not frame dependent) for instance. In which the table would be preventing the book from following its geodesic path. And in order to do that Work in the form of a quantity proportional to the EM force in the table material times distance from the theoretical geodesic path of the book, must be done.
I know is not the conventional way work is referred to in Newtonian physics(wich is the way you were defending it in your post, and as I said I perfectly understand the use of fictitious forces and work in Newtonian physics). But I think by introducing some GR ingredients in the situation it gets closer to reality.

 

[Dale]

Not exactly, KE is frame dependent, energy is a conserved quantity in Newtonian mechanics

All energy is frame dependent, not just KE. And yes, energy is conserved (in SR generally, in GR in static spacetimes). I think you may be mixing up conservation with frame invariance, they are two separate concepts. Energy is conserved, but frame variant.

(I understand you are restricting this to the Newtonian mechanics POV since you were talking about fictitious forces).

No, all of my comments above were wrt GR, not Newtonian physics. What makes you think that GR doesn't have ficitious forces? In fact, GR provides a very easy and consistent mechanism for determining fictitious forces through the Christoffel symbols.

http://en.wikipedia.org/wiki/Curvil...ous_forces_in_general_curvilinear_coordinates
http://www.mathpages.com/home/kmath641/kmath641.htm
http://theoretical-physics.net/dev/src/relativity/relativity.html#inertial-frames

And in order to do that Work in the form of a quantity proportional to the EM force in the table material times distance from the theoretical geodesic path of the book, must be done.

This is an incorrect definition of work. If you believe otherwise then please provide a mainstream scientific reference that defines work as the force times the "distance from the theoretical geodesic path".

I know is not the conventional way work is referred to in Newtonian physics(wich is the way you were defending it in your post, and as I said I perfectly understand the use of fictitious forces and work in Newtonian physics). But I think by introducing some GR ingredients in the situation it gets closer to reality.

No, all of my comments above are GR comments. In GR there are fictitious forces, just like in Newtonian mechanics. See the references above.

The difference is that in Newtonian mechanics gravity is considered a real force and in GR it is considered fictitious. I referred to mg as a fictitious force, so I was definitely discussing from the GR perspective. You are clearly misunderstanding how non-inertial frames and fictitious forces are treated in GR.

 

[TrickyDicky]

Great then, if you are considering gravity as a fictitious force then you indeed are using a GR perspective, sorry I didn't notice it. Yor conclusions made me think you were only considering the Newtonian view. But then you are reinforcing my point, thanks.
From wikipedia page on Fictitious forces:
"Fictitious forces can be considered to do work, provided that they move an object on a trajectory that changes its energy from potential to kinetic."
If the EM forces of the table (and the earth) didn't hold the book, it would spontaneously fly towards its geodesic path.

 

[Dale]

But then you are reinforcing my point, thanks.
From wikipedia page on Fictitious forces:
"Fictitious forces can be considered to do work, provided that they move an object on a trajectory that changes its energy from potential to kinetic."
If the EM forces of the table (and the earth) didn't hold the book, it would spontaneously fly towards its geodesic path.

Far from reinforcing your point, this completely contradicts your point. See the last two paragraphs of 316.

 

[TrickyDicky]

Those two paragraphs look wrong to me. You have the fictitious force of gravity on the book acting in an upward and downward direction at the same time on the same object. That is not possible.

 

[Dale]

Those two paragraphs look wrong to me. You have the fictitious force of gravity on the book acting in an upward and downward direction at the same time on the same object. That is not possible.

Nonsense. Where did I say that?

The fictitious force of gravity always acts downwards. In fact, it is what defines the direction "down". I never said anything to the contrary.

 

[TrickyDicky]

Nonsense. Where did I say that?

Now, work is f.d, so as an object is moved upwards against this fictitious force it requires an amount of work equal to f.d=mgh. Conversely, as an object is lowered the fictitious force does an amount of work equal to mgh.

Despite the fact that there is a force on the book (two forces actually) and the book measures a proper acceleration and is therefore non-inertial.

Here maybe it is your wording but you seem to have the book going up and down in a strange way, and you even transform the fictitious force into ¡two forces¡. Make up your mind, is the fictitious force of gravity one or two forces? is the book going up or down? I'm afraid it can't go up and down at the same time.

 

[Dale]

There are two forces acting on the book. One is the fictitious force of gravity, it points downwards and has a magnitude of mg. The other force is the real force from the table, it points upwards and also has a magnitude of mg. The two forces sum to zero so that there is no acceleration in the non-inertial reference frame.

I never once said that the fictitious force was pointing upwards.

 

[TrickyDicky]

There are two forces acting on the book. One is the fictitious force of gravity, it points downwards and has a magnitude of mg. The other force is the real force from the table, it points upwards and also has a magnitude of mg. The two forces sum to zero so that there is no acceleration in the non-inertial reference frame.

I never once said that the fictitious force was pointing upwards.

Well then you mixed them up to refer to the fictitious force of gravity and its effect on KE and PE.
Do you see now that if you consider gravity as a fictitious force and do not mix it up with the normal force, you have that the potential energy is being changed to kinetic energy (and this is the one that the normal force from the table counters to have an static situation from the Earth's frame, but if the table wasn't there the book would change its path)?

Consider the example in the wikipedia page:
"consider a person in a rotating chair holding a weight in his outstretched arm. If he pulls his arm inward, from the perspective of his rotating reference frame he has done work against centrifugal force. If he now let's go of the weight, from his perspective it spontaneously flies outward, because centrifugal force has done work on the object, converting its potential energy into kinetic. From an inertial viewpoint, of course, the object flies away from him because it is suddenly allowed to move in a straight line. This illustrates that the work done, like the total potential and kinetic energy of an object, can be different in a non-inertial frame than an inertial one."

 

[Q-reeus]

Others have already commented on this, but I would point out that "logic" requires axioms to start with, and requires a consistent set of propositions to be built up from those axioms. What I'm calling "math" is really a large set of such propositions built up from axioms, whose consistency has been carefully checked. But to carefully check that, you have to have an unambiguous way of expressing propositions, and an unambiguous way of expressing the logical connections between them. "Intuition" doesn't have any of that; it has propositions and logical connections expressed in English, which is not unambiguous, as I've pointed out before, and it certainly doesn't have a large consistent set of propositions whose consistency has been carefully checked.

[First off sorry about not responding earlier to this post but it somehow got missed, perhaps owing to a new page starting last postings of mine, and yours was not up on previous page when I composed last postings. Now to comment on the above and rest...]
Won't argue with the formalities there but it gets down to reasonableness versus unreasonableness. You received high praise from one recent poster for an answer in #287 that you may consider 'precise' but to my mind is just a string of words that asserts a generality without really explaining at all. It is trivially true that everything we experience originates from some 'past light cone(s)'. But where is the actual dynamical connection between exterior field point and inwardly hurtling charged matter asymptotically close to being completely engulfed within an EH? Mere details - as long as we accept it all comes from the past light cone, no problem at all! A matter of opinion perhaps, but I fail to be duly impressed with that.

On the other hand, if I make the point that for there to be any finite exterior BH E field, what most I think reasonably understand by 'gravitational redshift' can have no effect on any EH crossing charge acting as E field source (note this is not an RN situation but neutral BH fed by infall). A rather obvious conclusion I would have thought, but to you it is terribly imprecise and too intuitive to make any sense of. So, in frustration with that line of response, I furnished for your consideration and response numbers of what seems to me are perfectly straight-forward scenarios - examples in #272, #294, and you still manage to make them into 'confused', imprecise' situations somehow impossible to deal with. But let's continue.

As it happens, you go right on to give a good example:
Q-reeus: "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."

What does this mean, precisely? What is the "field transmitted from place to place"? What does "suffers zero reduction" mean? Try giving these things precise meanings, before asking us to accept your "intuition" about them. By "precise meanings" I mean actual observables. I've already described several such, and shown how they are all consistent.

I suspect you know very well what was meant, after so much discussion here - E field distribution is unaffected by gravity *if* RN BH is possible. Said on numerous occasions now and no *reasonable* room for doubt as to what I was once again pointing out.

Q-reeus: "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."

I already know your opinion? This test case is very different from what we have been discussing; what's the connection? Your "intuition" tells you they are connected? Can you give anything more precise than that? And what observable corresponds to the "field lines" of the charge?

You are kidding right? What in essence is different that so stumps you? Bottom line question to you clearly was - will field lines distort at all. And yes from umpteen previous postings you know exactly my view - of course there will be distortion occurring - but logically/intuitively not if one adheres to the RN-is-real view. And you have a problem knowing what 'distort' could possibly mean? Well there is just strength and direction to consider - and apart from using a standard 'test charge' there are lots of specialized detectors out there nowadays. But any excuse will do to avoid a straight answer - one that I suspect you sense will allow me to have you boxed in. A spot of paranoia on my part here is it? I sincerely hope so. Will give one more try at 'breakthrough' later on.

Q-reeus: "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?"

GR can tell you what the EM field tensor is due to the dipole. Is that what you mean by "dipole field strength"? Or it can tell you what the contraction of the EM field tensor is with some 4-vector. Is that what you mean by "dipole field strength"? Or do you mean something else?

Did I really need to elaborate? How freeking super precise do you need things to be - on certain occasions! Be reasonable please!

Q-reeus: "There is absolutely no experimental/observational support for a RN BH."

This is true. However, there is lots of experimental support for (1) the EFE as applied to spherically symmetric spacetimes; (2) the EM field tensor and the covariant form of Maxwell's equations as applied to electrodynamics under all conditions we have tested. R-N geometry is simply the result of combining the two.

Ah - "simply the result of combining the two". So absolutely no assumptions are made then as to *how* exactly the two are combined? You do recall I have hammered away on just that thing - beginning in #1?

Also, as has been said before, we can just as well consider the R-N geometry exterior to a charged massive object, rather than a BH. That involves only the R-N region exterior to the horizon, which avoids issues with what goes on inside the horizon, and is therefore an unproblematic solution of the EFE combined with Maxwell's equations.

Really. Well let's try it one more time - as best I care to try at being suffciently precise, here's yet another scenario and yet again ask your considered opinion:

There is an essentially 'point' electric dipole of moment p = qd and small mass m_p that initially lies motionless in notionally flat spacetime, and has a field distribution given here:
http://en.wikipedia.org/wiki/Dipole#Field_from_an_electric_dipole
We next assemble a spherical thin shell of mass M>>m_p and effective mean radius R, surrounding and centered on the dipole. Said mass is ideally transparent to dipole E field, and the sole possible effect of M on the dipole is via M's gravitational potential, and/or field external to R. We know the dipole lies in an equipotential region, depressed wrt infinity according to redshift factor (1-2GM/(Rc²)). So, if the dipole were to act as an oscillator, there is I trust no confusion over saying the emitted radiation will be redshifted by factor given above, as received by a distant observer. Now my hopefully crispy clear and concise question is - will the static dipole's field be in any way altered by the presence of M, as determined by a distant observer? That possible alteration is in field strength and/or field direction different to the 'before' case (you know - before we assembled M).
You do of course have a constitutional right to avoid and evade this question - or make it seem altogether too imprecise to handle. I cross fingers and hope for the best.

 

[Dale]

(and this is the one that the normal force from the table counters to have an static situation from the Earth's frame, but if the table wasn't there the book would change its path)?

I already explained exactly this situation in the third paragraph of 316. If an object is in free fall then the fictitious force does work on the object, changing its path (acceleration), gaining KE, and losing PE.

However, because the table is there the book does not accelerate, does not gain KE, and does not lose PE. No work is done on the book.

Consider the example in the wikipedia page:
"consider a person in a rotating chair holding a weight in his outstretched arm. If he pulls his arm inward, from the perspective of his rotating reference frame he has done work against centrifugal force. If he now let's go of the weight, from his perspective it spontaneously flies outward, because centrifugal force has done work on the object, converting its potential energy into kinetic. From an inertial viewpoint, of course, the object flies away from him because it is suddenly allowed to move in a straight line. This illustrates that the work done, like the total potential and kinetic energy of an object, can be different in a non-inertial frame than an inertial one."

Which again directly contradicts your claims and supports my claims.

I don't know how you are getting this stuff so wrong, I have already addressed every point that you are bringing up, and you seem to be misreading everything written either by myself or by anyone else. I think that you should start a new thread on the topic, I feel like we are hijacking Q-reeus' thread on something that is very tangential to his topic.

 

[TrickyDicky]

If an object is in free fall then the fictitious force does work on the object, changing its path (acceleration), gaining KE, and losing PE.

However, because the table is there the book does not accelerate, does not gain KE, and does not lose PE. No work is done on the book.

An object in free-fall doesn't accelerate in the GR perspective.
No work is done on the book in the Earth's frame and considering gravity a real force. But you are mixing the concept of gravity as real force and fictitious force according to your interest.

I won't continue this discussion with you. If you can't admit it when you are wrong is Ok with me I just wanted to clear that up for the benefit of Austin0 and possible other people reading.

 

[PeterDonis]

You received high praise from one recent poster for an answer in #287 that you may consider 'precise' but to my mind is just a string of words that asserts a generality without really explaining at all. It is trivially true that everything we experience originates from some 'past light cone(s)'. But where is the actual dynamical connection between exterior field point and inwardly hurtling charged matter asymptotically close to being completely engulfed within an EH?

The "dynamical connection" ("dynamical" is kind of an odd word to use since the spacetime is static, but I'll go with it here) is given by the EFE and Maxwell's equations. In the case of a neutral massive object collapsing to a Schwarzschild BH, the vacuum EFE determines how the spacetime curvature produced by the stress-energy in the object propagates through the vacuum region to any point. In the case of a charged massive object collapsing to a R-N BH, the EFE with a particular EM field tensor as source determines how the curvature produced by the stress-energy plus charge propagates, and Maxwell's equations determine how the EM field propagates. There is exact math behind all of it, just as I said.

On the other hand, if I make the point that for there to be any finite exterior BH E field, what most I think reasonably understand by 'gravitational redshift' can have no effect on any EH crossing charge acting as E field source (note this is not an RN situation but neutral BH fed by infall). A rather obvious conclusion I would have thought, but to you it is terribly imprecise and too intuitive to make any sense of.

Because I don't see any exact math behind it. I see you reasoning with intuitive concepts without going back to the fundamentals that underlie them. The fundamental laws, the EFE and Maxwell's equations, don't say anything about "redshift". That's a derived concept that can be used to label certain aspects of certain solutions. It may or may not apply in the case you're talking about.

So, in frustration with that line of response, I furnished for your consideration and response numbers of what seems to me are perfectly straight-forward scenarios - examples in #272, #294, and you still manage to make them into 'confused', imprecise' situations somehow impossible to deal with.

Same comment: I don't see the exact math behind them. You don't know any of the exact math, so you can't furnish it; and when I try to match up what you're saying to what I know of the exact math, I don't come up with a match. As I've said before in a discussion like this with you, if I read through one of your scenarios and I can't figure out how it fits into the math, even if what you are saying contains an apparent "paradox" with GR, my conclusion, if you force me to make one, will be that there is some mistake in your scenario that I'm not smart enough to spot, not that GR is wrong. The former is far more likely, IMO, than the latter. It's not that I'm not interested; it's just that if I can't figure out how to translate what you're saying into the fundamentals, the math, I have no way of telling whether it's right, wrong, or not even wrong. So what am I supposed to do?

E field distribution is unaffected by gravity *if* RN BH is possible.

And what does "E field distribution is unaffected by gravity" mean? I know you can't tell me what it means in the math, but can you at least say what specific observation I can make to tell me whether or not the E field distribution is affected? All the ones you've proposed so far have boiled down to an effect of transmitting something through a curved spacetime, which as I and others have said, is obviously due to the spacetime in between, not to the original "source" of what is being transmitted.

Bottom line question to you clearly was - will field lines distort at all.

And how do I tell, by observation/experiment, whether or not the field lines are "distorted"? Give a specific description set in your scenario, not just generalities about test charges and detectors. Why must I always do all the work?

Did I really need to elaborate?

Yes, because all the things I can come up with that "dipole field strength" could mean, GR can calculate for you, as I said, and none of them pose any contradiction. So if that's the best you can do, your example proves nothing.

Ah - "simply the result of combining the two". So absolutely no assumptions are made then as to *how* exactly the two are combined?

Not in the exact math; combining the two is simple and straightforward and requires no "assumptions" beyond the basics necessary to express any physical law in curved spacetime. All the GR textbooks I'm familiar with treat this exact case in some detail. MTW spends several chapters on it.

Well let's try it one more time - as best I care to try at being suffciently precise, here's yet another scenario

This seems to be your standard response in these discussions: when in doubt, pile on another scenario. :sigh:

I'll go ahead and take a look at this, but let's suppose that I come back and say that the radiation emitted by the dipole (which must be time-dependent to radiate, btw, I trust you've taken that into account even though it doesn't appear in your formulation) *is* redshifted when it is seen by an observer far away, as compared to how it is seen by an observer right next to the dipole. What will that prove?

To you, it will prove that somehow the R-N solution is inconsistent. To me, and probably to most others who are participating in this thread, it will mean that the curved spacetime in between the dipole and the observer has an effect on the radiation, just as one would expect, and will be perfectly consistent. What do we do then?

This is why these discussions always go on forever with no resolution.

 

[Dale]

An object in free-fall doesn't accelerate in the GR perspective.

This is only partly correct. In GR there are two different kinds of acceleration: proper acceleration and coordinate acceleration. An object in free fall has a 0 proper acceleration, but in a non inertial coordinate system it may have a non zero coordinate acceleration. That is essentially the defining characteristic of a non inertial frame.

No work is done on the book in the Earth's frame and considering gravity a real force. But you are mixing the concept of gravity as real force and fictitious force according to your interest.

No work is done on the book in the Earth's frame, period. It has nothing whatsoever to do with gravity being real or fictitious.

In non inertial frames fictitious forces can do work and be associated with a potential energy. I am not mixing the concepts at all, you just apparently don't understand how fictitious forces function.

I won't continue this discussion with you. If you can't admit it when you are wrong is Ok with me I just wanted to clear that up for the benefit of Austin0 and possible other people reading.

Why would I admit I am wrong when you haven't actually shown a single mistake in any of my comments? I haven't said anything incorrect and I have provided references to support. You have consistently misunderstood my comments, the references, and the physics.

Again, I recommend opening another thread in order to avoid hijacking Q-reeus' thread.