Steven Crothers , against BB

No, it isn't. That math isn't expressed in GR terminology.
Then you dispute the validity of GR metric values I gave as applying to particular cases? If not, what else GR-wise is relevant or needed to uncover the paradoxical conclusions?
I don't see how that's relevant? Many of the GR derivations can be done on paper; see for example that PDF you linked to.
You missed that the derivation contradicts that given by GR! But yes it is simple and can be done on paper. What I meant was, you would evidently insist one must labour away by setting up boundary and initial value conditions for the entire system - mass plus dipole say, and then try and solve that coupled system exactly via EFE's. I suggest a hopeless task and what's more a needless one. It can all be done on a semi-qualitative basis - just by looking at what is and isn't consistent if following basics of RN solution. Namely, that charge is supposedly unaffected by gravitational potential. Look at what that predicts in cases I gave.
Yes indeed, so you agree that GR is valid? (Seeing that that's the only theory mentioned in this thread that can explain it.)
Where did you get that idea from? Certainly not from a careful reading of what I have consistently presented here. See, the basic idea is to work within GR paradigm, and by doing so, uncover it's inconsistencies. Further, re RN type situation, the assumed charge invariance wrt gravity is something afaik generically adopted even by rival gravity theories. We don't really need to dispute exact correctness of redshift expression GR vs say Yilmaz gravity - it's good enough to use GR approximation - particularly in weak field situation where differences are negligible.

We have gotten to split the discussion from initial dispute over whether charge invariance logically holds in gravitational setting, into one over whether GR metric even for uncharged matter source is logically correct. Let's get back to just the RN/charge invariance issue.
Well, I'll have to dive into GR for details, but my guess would be that, since (almost) nothing is expressed in GR maths, it's some surprising feature of GR somewhere.
The challenge remains - point out specifically where I have made any incorrect assumptions that would invalidate conclusions.
The choice of metric is critical in GR. For example, the Schwarzschild metric has a singularity (which is physically weird), but the Minkowski metric has no such problems. Many of the "absurdities" in GR come from the choice of metric, not from GR itself.
Existence of both EH and singularity are generic features within GR and independent of choice of metric. Surely you know that. And as per that Appendix A - a pathology as consequence of adopting a truncated approximation for gravitational redshift. Correct expression inevitably yields the exponential Yilmaz metric. No weirdness to worry about there. Like I said, this is a fork from main argument over RN/charge invariance issue.
I know of no "GR gate-keepers" claiming this, and I agree with you that anybody who really claims this is not worth their salt in GR.
There are any number that do just that. I could point to many postings of GR buffs at PhysicsForums stating such but not much point in doing so.
Except for the infaller. Are you claiming the perspective of the infaller somehow becomes wrong as it crosses the event horizon?
On the face of it that line contradicts what you admit in the previous one. I guess it's so ingrained that proper time of infaller is all that matters.
Once again; coordinate speed of light c is zero at EH. Infaller never even gets to let alone passes through EH in finite coordinate time. And once again, this is a distracting fork off of RN/charge invariance issue.

Gravity is left out (out of EH) as fossil field, Spin is left out as angular momentum in ergosphere and charge is left out as eletrostatic field outside EH. This mathematical jugglery removes the obvious problem associated with infinite time dilation at or inside EH. You have to appreciate that Einstein never offered BH or such solutions around BH based on GR. It was the overenthusiastic crowd of mathematically oriented physicists who wanted to get into the GR / BH bandwagon. Now as somewhere you have rightly mentioned that the GR has become a 800 pounds gorilla, I would say after nobel on GW, it has doubled its crushing power. I ask a very simple question: the EHs (even for charged or rotating or both) will change its spatial position/size based on mass reduction (HR) or based on mass increase (accretion), the real impact of change in EH happens only after mass has entered the EH, then how does angular momentum or electrostatic filed reorient or realign due to change in EH?
The weird issues - even 'genuine' ones, stem from internal inconsistencies that unfortunately are still well enough hidden observationally, to have survived for over a century.

Q-reeus said:
Infaller never even gets to let alone passes through EH in finite coordinate time.
That's only true for external observers who don't get near the EH. The infalling object/observer sees nothing, according to GR, and simply accelerates towards the singularity (which is at future infinity).

That's only true for external observers who don't get near the EH. The infalling object/observer sees nothing, according to GR, and simply accelerates towards the singularity (which is at future infinity).
Future infinity (external, static observer time) is the point of getting to EH. According to pathological GR Schwarzschild metric. And it has a physical meaning and connection to outside. A notionally inextensible string, pulled say 1cm 'out there' at a static radius, will be recorded as the same 1cm motion 'down there' at a lower static radius. Proper and coordinate radial dispacement have a 1-to-1 correspondence. Attach such a string to an infalling object. Initially the string reeling 'out there' will accelerate, but strongly reducing value of √(g_tt) soon wins out. Coordinate c -> 0 and in consequence the string reeling motion 'out there' plummets rapidly towards zero. And stays that way for ever and ever and ever.
That's what it physically means to say the infaller never even gets to the EH.

Well the Newtonian potential just keeps on getting deeper and deeper 'inside' of EH. Assuming 'inside' has any sensible meaning. Do you suppose time then sort of reverses or something, instead of becoming - what - infinitely infinitely redshifted? The craziness of such a situation should be ringing alarm bells.

Compare that to working from Yilmaz metric - the rational outcome of applying the exact results in that Appendix A referenced earlier. There is no infinitely redshifted EH, but still an asymptotically approached singularity of sorts as r -> 0. But a soft one vs the hard one of GR.
Soft because as shown elsewhere, it's curvature scalar is zero not infinite as it is in GR. Which afaik stems from that the proper distance to the notional singularity at r = 0 is infinite in Yilmaz metric. Requiring therefore infinite proper time for unimpeded free-fall to r = 0. Which is in a way 'safe' but unrealistic as it assumes idealized 'dust' as prior collapsed matter source that never offers any resistance to crushing. Hence only vacuum encountered all the way down to r = 0 for infaller as 'test particle'.
In a realistic setting where matter has offered resistance, one should expect Yilmaz metric sensibly allows both finite coordinate and proper times for infall to some compact and stable finite sized end-point region. As √(g_tt) only approaches but never realistically goes to zero, at no stage is the infaller causally cut off from the outside. No infinities. No weird 'interior metric' with 'infalling spacetime' etc.

And this is a continued fork from the main issue of RN metric with it's having charge independent of gravitational potential.

Then you dispute the validity of GR metric values I gave as applying to particular cases? If not, what else GR-wise is relevant or needed to uncover the paradoxical conclusions?
No, I am suspicious because there are many surprising features hiding in the maths of GR, that only become apparent when you use the proper formulation.

You missed that the derivation contradicts that given by GR!
Please point me to this derivation using GR terminology that I have missed.

But yes it is simple and can be done on paper. What I meant was, you would evidently insist one must labour away by setting up boundary and initial value conditions for the entire system - mass plus dipole say, and then try and solve that coupled system exactly via EFE's.
Yes, properly defining and describing the situation is important in physics.

I suggest a hopeless task and what's more a needless one.
You think it's OK to work with an ill-defined environment?

It can all be done on a semi-qualitative basis - just by looking at what is and isn't consistent if following basics of RN solution.
And to do that properly, one must use GR terminology and maths in order to make sure all effects are taken into account. It's easy to miss one of the more surprising features otherwise.

Namely, that charge is supposedly unaffected by gravitational potential. Look at what that predicts in cases I gave.
(Already discussed; no comment for now.)

Where did you get that idea from? Certainly not from a careful reading of what I have consistently presented here.
You said in post #138 that "gravitational redshift aka time dilation is experimentally confirmed." The only theory I know of that can explain this is GR. In face, it's a prediction of it. By carefully analyzing the wording, especially the use of the word "confirmed", I can only come to the conclusion you agree with the validity of GR.
I realize that seems to contradict what you said earlier, so can you please carefully reword what you said in post #138 to resolve this?

See, the basic idea is to work within GR paradigm, and by doing so, uncover it's inconsistencies. Further, re RN type situation, the assumed charge invariance wrt gravity is something afaik generically adopted even by rival gravity theories. We don't really need to dispute exact correctness of redshift expression GR vs say Yilmaz gravity - it's good enough to use GR approximation - particularly in weak field situation where differences are negligible.
Yes, and as I've already pointed out: one needs to be careful whether the inconsistencies are coming from GR itself, or from the choice of metric.

We have gotten to split the discussion from initial dispute over whether charge invariance logically holds in gravitational setting, into one over whether GR metric even for uncharged matter source is logically correct. Let's get back to just the RN/charge invariance issue.
OK

The challenge remains - point out specifically where I have made any incorrect assumptions that would invalidate conclusions.

Existence of both EH and singularity are generic features within GR and independent of choice of metric. Surely you know that.
Please point out the event horizons and singularities in the Minkowski metric.

And as per that Appendix A - a pathology as consequence of adopting a truncated approximation for gravitational redshift. Correct expression inevitably yields the exponential Yilmaz metric. No weirdness to worry about there. Like I said, this is a fork from main argument over RN/charge invariance issue.
(No comment as I have to dive into GR first.)

There are any number that do just that. I could point to many postings of GR buffs at PhysicsForums stating such but not much point in doing so.
Their misunderstanding of GR is their own problem; let's indeed not pay any further attention to (self-proclaimed?) anonymous "GR buffs".

On the face of it that line contradicts what you admit in the previous one. I guess it's so ingrained that proper time of infaller is all that matters.
Once again; coordinate speed of light c is zero at EH. Infaller never even gets to let alone passes through EH in finite coordinate time. And once again, this is a distracting fork off of RN/charge invariance issue.
But the local speed of light for the infaller is still c. The infaller still sees the black hole approaching fast in proper time. There's no contradiction that an observer infinitely far away sees that the infaller never reaches the event horizon, while the infaller passes the location of the event horizon without incident. This is a basic SR thing.

You said in post #138 that "gravitational redshift aka time dilation is experimentally confirmed." The only theory I know of that can explain this is GR.
Yilmaz gravity and various other metric theories all predict the same weak field redshift. Nothing unique to GR about that. Strong field predictions a different matter. Hope that clears that one up.
Please point out the event horizons and singularities in the Minkowski metric.
I was simply being careless to not actually write 'choice of coordinate system e.g Gullstrand–Painlevé, standard Schwarzschild etc.'. Often btw expressed as 'such-and-such a metric'.

Yilmaz gravity and various other metric theories all predict the same weak field redshift. Nothing unique to GR about that. Strong field predictions a different matter. Hope that clears that one up.
But Yilmaz is (even more?) internally inconsistent than GR, going by the Wikipedia entry:
https://en.wikipedia.org/wiki/Yilmaz_theory_of_gravitation
Yilmaz's work has been criticized on the grounds that
- his proposed field equation is ill-defined,
- event horizons can occur in weak field situations according to the general theory of relativity, in the case of a supermassive black hole.
- the theory is consistent only with either a completely empty universe or a negative energy vacuum.
I can hardly can that a valid alternative...

I was simply being careless to not actually write 'choice of coordinate system e.g Gullstrand–Painlevé, standard Schwarzschild etc.'. Often btw expressed as 'such-and-such a metric'.
OK.

Q-reeus said:
That's what it physically means to say the infaller never even gets to the EH.
But the infalling observer does get to the EH, and passes through it with no physical problem. You might be overlooking that the infalling observer is in an accelerated frame, whereas an external 'static' observer is in a completely different frame.

That's one reason that it makes no sense to talk about "inside the event horizon" for an external observer, whereas according to known laws of physics, an infalling observer just accelerates, although will be subject to extreme tidal forces.

Does it make sense to talk about infalling radiation with a given wavelength? Sure it does; it even makes sense to compare wavelengths with the radius of the black hole's EH (given some metric). And it makes sense to talk about how short a wavelength for photons an external observer can project towards an infalling object, to (try to) determine where it is.

But Yilmaz is (even more?) internally inconsistent than GR, going by the Wikipedia entry:
https://en.wikipedia.org/wiki/Yilmaz_theory_of_gravitation
Yilmaz's work has been criticized on the grounds that
- his proposed field equation is ill-defined,
- event horizons can occur in weak field situations according to the general theory of relativity, in the case of a supermassive black hole.
- the theory is consistent only with either a completely empty universe or a negative energy vacuum.
I can hardly can that a valid alternative...
Going by that Wikipedia entry....written by the GR fanatical devotee Chris Hillman, who evidently considers it a sacred duty to put down all alternatives to GR.
You did notice and read the prominent warning passage preceding the actual article? No?

The 1st point - supposed ill-defined eqns, is itself ill-defined. In further links there, you will find articles by Misner and Fackerell claiming to pick holes in Yilmaz gravity. But there are also links to point-by-point responses by Yilmaz And Alley. To which neither Misner or Fackerell responded back. Why not rather study what the extant expert on Yilmaz gravity has to say:
https://arxiv.org/abs/1606.01417
http://arxiv.org/abs/1507.07809
He covers everything claimed to be a flaw in YG, and shows how the claims are what's flawed - partly owing to incorrect analyses and faulty conclusions thereby drawn by previous workers in the field.

The 2nd point - 'weak field situations' cherry picks a definition not used by others - namely that tidal gravity is weak - for an arbitrarily supermassive BH. But it's the value of √(g_tt) that most consider the marker of 'strong field' and that's always 0 at EH of BH of any size.

3rd point is covered above - read in particular part 4 Discussion in: http://arxiv.org/abs/1507.07809

Finally, I'll remind that an exact derivation of gravitational redshift, appendix A in https://arxiv.org/abs/1606.01417
is what shows GR to be fundamentally flawed. An aesthetic choice by AE demanding 'pure geometry' for his spacetime formulation meant he simply ignored the dictates of that exact requirement for redshift. One demanding an exponential metric free of EH's and all the craziness associated with such.

But the infalling observer does get to the EH, and passes through it with no physical problem. You might be overlooking that the infalling observer is in an accelerated frame, whereas an external 'static' observer is in a completely different frame.

That's one reason that it makes no sense to talk about "inside the event horizon" for an external observer, whereas according to known laws of physics, an infalling observer just accelerates, although will be subject to extreme tidal forces.

Does it make sense to talk about infalling radiation with a given wavelength? Sure it does; it even makes sense to compare wavelengths with the radius of the black hole's EH (given some metric). And it makes sense to talk about how short a wavelength for photons an external observer can project towards an infalling object, to (try to) determine where it is.
I'm afraid we simply see it all differently. You wish to concentrate exclusively on the infaller proper time pov. I have pointed out what it means to ignore ramifications of the global aka coordinate perspective.

The weird issues - even 'genuine' ones, stem from internal inconsistencies that unfortunately are still well enough hidden observationally, to have survived for over a century.

Yes, they have survived.
There is no answer in the literature, how the angular momentum (as preserved in the ergosphere) or electrostatic field outside outer Event Horizon....realign or reconfigure when there is any change in these horizons size due to mass accretion. The point is mass accretion can be reflected only when the mass has entered the event horizon, not before, so any change in alignment of angular momentum or electric field, cannot happen unless it is causally changed by some mechanism inside EH, which is forbidden.

I'm afraid we simply see it all differently. You wish to concentrate exclusively on the infaller proper time pov. I have pointed out what it means to ignore ramifications of the global aka coordinate perspective.

Infaller proper time pov is meaningless concept, simply because any delta t inside will be infinite time for the outside observer. So for outsiders the observer can never go beyond EH. And we talk of mass accretion by BHs and real time manifestation of the same, all convenient maths, one step contradicting the other.

Yes, they have survived.
There is no answer in the literature, how the angular momentum (as preserved in the ergosphere) or electrostatic field outside outer Event Horizon....realign or reconfigure when there is any change in these horizons size due to mass accretion. The point is mass accretion can be reflected only when the mass has entered the event horizon, not before, so any change in alignment of angular momentum or electric field, cannot happen unless it is causally changed by some mechanism inside EH, which is forbidden.
Leaving aside 'electrostatic field issue' which I have been trying unsuccessfully to again become the focus, that there is any angular momentum at all for a Kerr-type BH is problematic in GR. It's necessary to do a maths trick and rob Peter to pay Paul. Don't ask for details. I want to get back to RN solution. Or just abandon another evident hopelessly sidetracked fizzler thread.

Infaller proper time pov is meaningless concept, simply because any delta t inside will be infinite time for the outside observer. So for outsiders the observer can never go beyond EH.
Some of the 'old timers' like iirc Dirac recognized the problem and maintained there was no meaningful inside. Which at least is a consistent position from within GR paradigm.
And we talk of mass accretion by BHs and real time manifestation of the same, all convenient maths, one step contradicting the other.
Mass accretion per se is not a real problem. As for how to 'expand the EH', here is one attempt at making sense of it: http://mathpages.com/rr/s7-02/7-02.htm
I don't waste much time on such stuff. Being satisfied the foundations are somewhat sandy.

Going by that Wikipedia entry....written by the GR fanatical devotee Chris Hillman, who evidently considers it a sacred duty to put down all alternatives to GR.
You did notice and read the prominent warning passage preceding the actual article? No?

The 1st point - supposed ill-defined eqns, is itself ill-defined. In further links there, you will find articles by Misner and Fackerell claiming to pick holes in Yilmaz gravity. But there are also links to point-by-point responses by Yilmaz And Alley. To which neither Misner or Fackerell responded back. Why not rather study what the extant expert on Yilmaz gravity has to say:
https://arxiv.org/abs/1606.01417
http://arxiv.org/abs/1507.07809
He covers everything claimed to be a flaw in YG, and shows how the claims are what's flawed - partly owing to incorrect analyses and faulty conclusions thereby drawn by previous workers in the field.

The 2nd point - 'weak field situations' cherry picks a definition not used by others - namely that tidal gravity is weak - for an arbitrarily supermassive BH. But it's the value of √(g_tt) that most consider the marker of 'strong field' and that's always 0 at EH of BH of any size.

3rd point is covered above - read in particular part 4 Discussion in: http://arxiv.org/abs/1507.07809

Finally, I'll remind that an exact derivation of gravitational redshift, appendix A in https://arxiv.org/abs/1606.01417
is what shows GR to be fundamentally flawed. An aesthetic choice by AE demanding 'pure geometry' for his spacetime formulation meant he simply ignored the dictates of that exact requirement for redshift. One demanding an exponential metric free of EH's and all the craziness associated with such.
So when comparing GR and Yilmaz, it's quite clear GR fits the observational data quite nicely, while there is still a lot of discussion about Yilmaz gravity. Even if it can model a thing or two, it's not clear (yet) whether it can do as well as GR. As I said, I can hardly call that a valid alternative...

So when comparing GR and Yilmaz, it's quite clear GR fits the observational data quite nicely, while there is still a lot of discussion about Yilmaz gravity. Even if it can model a thing or two, it's not clear (yet) whether it can do as well as GR. As I said, I can hardly call that a valid alternative...
As you wish. I think this thread should just go to sleep.

I may have located a problem. Shouldn't the dr also change due to length contraction in the gravitational field?
No firstly because in my given example the dipole axis is orthogonal to a radius vector eminating from the centre of mass. The proper dr and coordinate dr are then explicitly identical - transverse spatial metric components in standard Schwarzschild chart are totally independent of gravity. Besides, even if oriented radially, as I mentioned elsewhere, there is also a 1:1 correspondence between proper and coordinate radial displacements in that case. If not, one could construct a cyclic perpetuum mobile. Think about it.
Here's a post explaining it much better than I can at this moment: https://physics.stackexchange.com/q...action-in-a-gravitational-field/145304#145304
That may appear to conflict with what I wrote above but does not. I'm well aware of how the 'areal radius' is reckoned in standard Schwarzschild coordinates. That space is locally non-Euclidean and there are more proper radial units between surfaces of given area ratio than in flat space has no bearing on the equality of proper and coordinate radial displacements. A tape measure will reel out more cm say in measuring between two concentric surfaces than in flat space, but a radial displacement 'out there' is recorded as the same radial displacement 'down there'.

Bottom line; 'redshifting' of energy in given dipole displacement scenario, which must be the case, necessarily implies 'redshifting' of either q or E or both.

To repeat from much earlier: That a BH can supposedly carry an externally felt charge automatically implies a static E (or B) field cares nothing for the spacetime metric generated by that BH mass. And I have previously cited passages from accepted articles stating as much. Strange that. Because all agree EM radiation has no such immunity and will undergo redshift and deflection as the metric dictates. Very strange contrast indeed.

No firstly because in my given example the dipole axis is orthogonal to a radius vector eminating from the centre of mass. The proper dr and coordinate dr are then explicitly identical - transverse spatial metric components in standard Schwarzschild chart are totally independent of gravity.
What transverse spatial metric components? The distance between the two plates in a spherical capacitor is parallel to the r-coordinate, not transverse. So the dr between plates has the same direction as the r-coordinate.

Besides, even if oriented radially, as I mentioned elsewhere,
Ah, you've given multiple scenario's. I was using post #79; that's also from where I got that quote.

there is also a 1:1 correspondence between proper and coordinate radial displacements in that case. If not, one could construct a cyclic perpetuum mobile. Think about it.
I will, but the linked post strongly suggests that your assertion here may be incorrect. Can you back up your claim that the proper and coordinate radial displacements correspond 1:1?

That may appear to conflict with what I wrote above but does not. I'm well aware of how the 'areal radius' is reckoned in standard Schwarzschild coordinates. That space is locally non-Euclidean and there are more proper radial units between surfaces of given area ratio than in flat space has no bearing on the equality of proper and coordinate radial displacements. A tape measure will reel out more cm say in measuring between two concentric surfaces than in flat space, but a radial displacement 'out there' is recorded as the same radial displacement 'down there'.
How can a measuring stick record a larger displacement, but the displacement isn't larger? That seems weird to me (assuming a rigid measuring stick, of course).

Bottom line; 'redshifting' of energy in given dipole displacement scenario, which must be the case, necessarily implies 'redshifting' of either q or E or both.[/QUOTE]
Isn't it possible that the energy of the E-field gets redshifted too, without the field itself getting changed? (Just thinking out loud here.)

To repeat from much earlier: That a BH can supposedly carry an externally felt charge automatically implies a static E (or B) field cares nothing for the spacetime metric generated by that BH mass. And I have previously cited passages from accepted articles stating as much. Strange that. Because all agree EM radiation has no such immunity and will undergo redshift and deflection as the metric dictates. Very strange contrast indeed.
As previously stated, I agree with you that this seems weird.

What transverse spatial metric components? The distance between the two plates in a spherical capacitor is parallel to the r-coordinate, not transverse. So the dr between plates has the same direction as the r-coordinate.
As you figured below I was referring to the dipole case not spherical capacitor - but in the end it doesn't matter.
I will, but the linked post strongly suggests that your assertion here may be incorrect. Can you back up your claim that the proper and coordinate radial displacements correspond 1:1?
It's quite straightforward. While from a coordinate basis the radial spacing of transverse grid lines compress closer to the source mass, radially oriented ruler shrinks by exactly the same fraction. The two cancel at any given radial location. Hence a 1cm proper radial displacement at one elevation is always transmitted as a proper 1cm radial displacement at any other elevation (we ignore 'practical' matters like mechanical stress/strain, and of course that elevations are always above the dreaded 'EH').
Again - that there are more intervening radial units in the gravity effected case (recall that is based on proper radial distance between shells of specified area ratios.) has no bearing on that.
How can a measuring stick record a larger displacement, but the displacement isn't larger? That seems weird to me (assuming a rigid measuring stick, of course).
See above.
Isn't it possible that the energy of the E-field gets redshifted too, without the field itself getting changed? (Just thinking out loud here.)
That implies it's the free-space permittivity/permeability that 'really' alters for field energy densities Ue = 0.5εE², Ub = 0.5B²/μ.
Since both Ue and Ub redshift by factor √(g_tt), then ε -> ε√(g_tt), while μ -> μ/√(g_tt) according to that idea. Epsilon declines, mu increases - all on a coordinate not proper basis obviously.

Now c is also defined in free-space by c = 1/√(εμ). From above that means coordinate value of c should alter by factor 1/√(√(g_tt)/√(g_tt)) = 1. In other words it predicts c is unaffected by the metric. Doesn't look right to me. We could look at the predicted coordinate value for free-space impedance and it's implications, but finding for c is enough.
As previously stated, I agree with you that this seems weird.
That's a polite way of putting it.

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