Is 'charged black hole' an oxymoron?

[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.

 

[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.