After Hawking, how "black" is a black hole?

[Yablon]

Hi to all,

I just posted my second YouTube talk, titled "After Hawking, how "black" is a black hole?" You may watch at this link: https://youtu.be/w1lPPR7_kwA.

Feedback and suggestions are welcome.

Best to all,

Jay

[ben6993@hotmail.com]

Hi Jay

Very good. Also good to see you in movies. I have viewed both of them and they are fine imo.

It might be better to save your Word doc of notes as a pdf? The hbar symbol ruins the maths formulae when I view on my ipad though it is perfectly OK when I view on my desktop PC which has MS Office installed. Also, you might need to give the link for every such document as I could not find it for the BH talk.

Thank you for making Hawking radiation seem much more plausible. I was rather sceptical about them after seeing Susskind's GR lectures ten years ago.

[Yablon]

Hi Jay

Very good. Also good to see you in movies. I have viewed both of them and they are fine imo.

It might be better to save your Word doc of notes as a pdf? The hbar symbol ruins the maths formulae when I view on my ipad though it is perfectly OK when I view on my desktop PC which has MS Office installed. Also, you might need to give the link for every such document as I could not find it for the BH talk.

Thank you for making Hawking radiation seem much more plausible. I was rather sceptical about them after seeing Susskind's GR lectures ten years ago.

Thanks Ben. I had problems with WordPress rendering the PDFs at all (their error, I believe), and YouTube does not have any facility (at least that I could find) for uploading PDF. I will need to find another venue to upload to, or maybe I'll just put the notes into a JPG then onto WordPress. Other (simple) ideas for making those generally available? Jay

[ben6993]

Hi Jay

Using JPG would solve the matter. I have this morning tried to upload a PDF file to my (free) wordpress site and failed. There are about ten acceptable file types but PDF isn't one of them. I doubt that there is a simple solution.

[kev01]

Sorry Jay but imo an exact analysis of Einstein's elevator EP gedanken experiment establishes (at least in the limit of negligible gravitational field self-gravitation) that the correct metric is an exponential horizonless one:
https://arxiv.org/abs/1606.01417 Appendix A
Beginning with slide 8 and ending at slide 19, the same result is methodically derived via a slightly different 'k-calculus' route here:
https://www.powershow.com/view/1bbc8-Zjh...esentation
There's a completely different analysis, paradoxically done at the very weak field regime, that clinches the need for a strictly spatially isotropic metric analog to asymmetric Schwarzschild one of GR. The so-called 'isotropic' version of SM is a fake one-point 'transformation', but it took me quite a while to finally realize that resolution.

[Yablon]

Sorry Jay but imo an exact analysis of Einstein's elevator EP gedanken experiment establishes (at least in the limit of negligible gravitational field self-gravitation) that the correct metric is an exponential horizonless one:
https://arxiv.org/abs/1606.01417 Appendix A
Beginning with slide 8 and ending at slide 19, the same result is methodically derived via a slightly different 'k-calculus' route here:
https://www.powershow.com/view/1bbc8-Zjh...esentation
There's a completely different analysis, paradoxically done at the very weak field regime, that clinches the need for a strictly spatially isotropic metric analog to asymmetric Schwarzschild one of GR. The so-called 'isotropic' version of SM is a fake one-point 'transformation', but it took me quite a while to finally realize that resolution.

Hi Kev:

The main point of my YouTube talk https://www.youtube.com/watch?v=w1lPPR7 ... e=youtu.be is that a Schwarzschild black hole, based on a "particle in a box" analysis, will withhold photons with wavelengths shorter than the event horizon diameter of that black hole (whereby for that portion of the spectrum the black hole remains "black" notwithstanding Hawking radiation emissions at lower wavelengths), and that based on Hawking's relation for the black hole spectral temperature, the cutoff wavelength between photons which are emitted and those that are withheld is at about 1/8 of the Wien displacement peak. At about 32 minutes into his lecture https://www.cornell.edu/video/leonard-s ... -principle, Susskind employs the same analysis to show how the Hawking radiation relation is derived, when he talks about longer-wavelength photons "bouncing off" a black hole, and says how for a photon to be absorbed it has to have a wavelength that is short enough. He is clear that he leaves out constants of proportionality which are close to 1 just to simplify his lecture. But if one is precise and leaves those constants in, then the photons which are absorbed have to have wavelengths shorter than the black hole diameter, and those that bounce off will have longer wavelengths.

Do you see any flaw in that analysis?

Jay

[kev01]

Hi Jay,
I'll try and get straight to the point. The entire HR/BH 'information paradox' and related 'Unruh effect' etc. sub-industry as it has become, relies on the existence of supposed 'horizons'. A BH 'event horizon' in the gravitational context, and a Rindler 'horizon' in the acceleration-in-flat-spacetime context.
The two articles I have earlier linked to show that an exact treatment of Einstein's Elevator gedanken experiment does not allow for any such horizons.
Light can always escape from a gravitationally collapsed mass - but from an extremely narrow cone window and extremely redshifted. It will though look just like a 'BH'. A so-called 'BH imitator'.
You may think such a relatively low-level math finding would have been acted upon way back at the outset of GR or even before its 1915-16 publishing.
Again - the two articles delve into some of the history on that.

I mentioned an alternate analysis that shows unambiguously that spatially anisotropic Schwarzschild metric cannot be correct. Rather than point to my old (and needing much tidying up) vixra article on that, here's a challenge for you. Won't be hard.

Consider a thin spherical self-supporting shell - say a typical old-style steel 'toy globe' shorn of support structure. Exterior metric according to GR is of course the Schwarzschild one. In the interior, it's necessary to correspond to the Newtonian limit of flat spacetime equipotential region.
Hence a transition from an exterior anisotropic SM -> isotropic and perfectly flat Minkowsi metric inside. No need to try and 'sculpture' the transition metric within the shell wall. Doesn't matter here. What does matter is the logical implications of exterior vs interior metrics. We note from standard SM that in that exterior region, transverse spatial metric components have no dependence on central mass determined Newtonian potential. Always have the gravity free values.
By contrast, both the scalar, temporal component, and radial spatial component, are functions of the Newtonian potential. In fact if one casts the temporal component into a clock-rate (frequency redshift form) inverse of the traditional dilation (wavelength redshift form), it's immediately evident both have IDENTICAL Newtonian potential dependence there.

BUT - 'magically' - in the flat interior region, while all agree coordinate clock-rate continues to be depressed wrt zero gravity case, spatial flatness FORCES an illogical vanishing of potential dependence of radial spatial metric. It HAS to somehow adopt the same potential independent value of the transverse spatial components!
Think about whether sensible, internally consistent physics is prevailing there. Or whether we have a clear case of an illogical force-fit based on assuming SM is true.

I took it one step further. Given the almost perfect linearity in that extremely weak gravity regime, do a straightforward summation over the shell mass, of elemental contributions to the interior metric at the dead center. Assume each elemental shell mass generates it's own SM, that can then be linearly added together with negligible final error. A particularly easy task and the 'surprising' result is an obviously isotropic, *depressed* spatial interior metric - amplitude of depression 1/3 that of radial spatial metric component at the exterior surface of assumed very thin shell.

I'll leave it to you to choose whether to conduct your own analysis and see if we have matching findings.

Do the same evaluations for Yilmaz spatially isotropic metric and it's very obvious no such conundrums arise. Just nice, paradox-free self-consistency.

[kev01]

There has been, how to say this, a protracted pause this thread. For whatever reason(s). Maybe this will kick-start further dialog:
In post #5 (there is unfortunately no actual, convenient post numbering protocol in place): viewtopic.php?p=849#p849
It was asserted without actual justification:
"The so-called 'isotropic' version of SM is a fake one-point 'transformation', but it took me quite a while to finally realize that resolution."

Not at all hard to justify that claim. One only has to examine the form of the standard, anisotropic SM, contrasted with the 'isotropic form':

https://physics.stackexchange.com/quest ... oordinates

The standard form is clearly non-Euclidean, i.e. locally there is 1st order departure from the flat spacetime Euclidean requirement dA/dr = 2π, where A is area of a shell at radius r. Owing to that the GR Schwarzschild redshift metric operator √(1−2𝑚/𝑟)^−1 acts only on the radial not transverse spatial components. Thus there is, at least in principle, a physically determinable non-Euclidean measure. This would mean that e.g. more tiny marbles could be packed in the volume between two concentric radial shells of a given locally measured radial separation, than in the corresponding flat Euclidean case.

Compare that situation to the so-called 'isotropic' form, where by definition of being 'isotropic', the metric operator (1+𝑀/2𝑟′)^2 acts EQUALLY on ALL spatial components. Thus, regardless of how wildly the metric operator varies with transformed radius variable r', the result is guaranteed to be a locally 1st order Euclidean spacetime.
Thus, to first order in the metric expansion, marble packing will correspond to Euclidean formula.

Obviously, something is amiss.
In a now abandoned forum, another member provided a standard derivation of the usual transformation from standard anisotropic SM to ISM:
http://www.sciphysicsforums.com/spfbb1/ ... t=77#p3408
I struggled to find a logical hole in that formally mathematically correct derivation. But much later....

By sheer luck or providence or whatever, stumbled across:

https://www.gsjournal.net/Science-Journ ... nload/1738

2. One-Point and Two-Points Transformations of Coordinates

The gist there is that a formal transformation from say standard SM to 'isotropic' SM, as linked to above, can be mathematically correct but physically misleading.
Being actually just a mapping of a single point only (or constant r surface in SM case) in one coordinate chart to a corresponding point (or constant r surface) in the new coordinate chart. Expand over a finite volume (thus where r necessarily varies), then transform that volume back to the old coordinate chart, and there is no longer an exact correspondence.

This mismatch HAS to be so for Schwarzschild transformations since for sure the standard form is locally non-Euclidean to first order in metric derivative, whereas the 'isotropic' form pretends to be locally Euclidean to first order by inspection of it's form. A physical distinction.

Yilmaz metric is inherently locally Euclidean to first order in metric derivatives. That is, dA/dr = 2π.

[kev01]

For some reason I was not permitted to edit above post even though it was posted a few minutes prior! Anyway, I should have written
dA/dr = 2πr wherever I wrote dA/dr = 2π. Sorry for error. Also, in two places the transformed r' symbol (signifying transformed 'isotropic' Schwarzschild radial coordinate) should have been used rather than r (for standard form Schwarzschild coordinate chart).

[kev01]

Regarding my careless posting error two post ago re Euclidean requirement dA/dr = 2πr, (not 2π). I was actually thinking of a more compact and dimensionless way of expressing the situation.
Namely, take any 'great circle' on a shell of given area A = 4πr^2 thus 'great circle' circumference C = 2πr = A/(2r), then
dC/dr = 2π (Euclidean metric)
Which is dimensionless. GR's Schwarzschild metric does not conform to that simple dimensionless locally Euclidean requirement.

[kev01]

Lucky for me what has descended into a one-sided conversation allows space to fix some errors persisting from earlier posts here.
Firstly, given Euclidean flat spacetime, the correct differential relation between area A = 4πr^2 of a spherical shell of radius r is
dA/dr = 8πr
The corresponding differential relation between circumference C of a great circle on that sphere, and radius r is
dC/dr = 2π
For exterior SM, the proper distance dr between two closely spaced concentric great circles of given circumferences C2, C1, is greater than in the Euclidean case by a factor

√(-g_rr) = 1/√(1-2GM/r) ~ 1/(1-GM/r) for 2GM/r << 1
(see last answer in https://physics.stackexchange.com/quest ... oordinates)

Thus the rate of change of proper C with proper r will be less than in the Euclidean case by the inverse:

dC/dr (proper, SM) = 2π√(1-2GM/r) ~ 2π(1-GM/r)

Which persists as a less than 2π constant value as dr -> 0.
Always less fractional difference in proper circumferences between the circles, for a given proper dr, than in the Euclidean flat spacetime case.
Alternately, always more (planar) proper area enclosed between the circles for a given differential in proper circumferences, than in flat spacetime.
Physically measurable intensive properties - in principle at least. According to GR.

For both the 'isotropic' SM, and Yilmaz inherently isotropic metric, the limit is Euclidean value 2π exactly for dC'/dr', dC/dr, respectively, as dr', dr, -> 0.
Since by the very meaning of (local) isotropy, the metric operator √(-g_rr) acts equally in both numerator (on dC' dC) and denominator (on dr', dr).

Hopefully no blunders made this round! Feel free to jump in and point any out though.

[kev01]

Well I can either claim my use of gravitating source mass M last post was the 'reduced mass' M/c^2, or admit I left out a factor c^2 in the expression for g_rr. Sorry.
The usual expression is of course (+--- convention) g_rr = -1/(1-2GM/(rc^2))

[kev01]

A hopefully properly cleaned up summary of imo reasons why GR's SM (Schwarzschild metric) cannot be correct.

1: A rigorous treatment of Einstein's Elevator EP gedanken experiment, as linked to in earlier post
viewtopic.php?p=849#p849
leads to the Yilmaz horizonless exponential metric with time-time metric component g_tt having the standard form exp(2GM/(rc^2)).
Not the GR SM equivalent g_tt = 1-2GM/(rc^2), with its pathological infinite redshift 'coordinate singularity' i.e. 'event horizon' at r_s = 2GM/c^2.

2: Evaluation of the transition from exterior SM to interior MM (Minkowski metric) for a gravitationally very small thin self-supporting spherical shell, as in post
viewtopic.php?p=851#p851 ,
reveals a fundamental lack of self-consistency. There is no physically justifiable explanation for the selective vanishing of Newtonian potential dependence, for the radial spatial metric component g_rr only, everywhere within the spatial flat spacetime valued hollow interior region. Not shared by the temporal component g_tt.
Why should coordinate values of rulers and clock experience a fundamentally different treatment? Only as an artifact of an internally inconsistent SM.

We observe by simple inspection the isotropic Yilmaz metric suffer no such internal inconsistency - there is a perfectly smooth transition of ALL metric components from exterior to interior region. No illogical selective vanishing, no bumps and jumps to scratch head over. Clocks and rulers experience precisely the same coordinate valued depression wrt gravity-free case.

3: Sticking with the same shell arrangement, consider a single 'point' element of shell mass, and take it as a source of SM in it's own right. Then it's immediately apparent, even without performing a straightforward (tensor addition, linear regime) integration over the entire shell mass, that any such mass element will induce a depressed value of spatial metric at the shell dead center. Owing to the radial spatial contribution. Which contradicts the standard GR requirement of not just flat spacetime in the interior region, but necessarily the gravity-free value also. Fundamental internal inconsistency once again!
One could perform a more elaborate evaluation at arbitrary hollow interior region radii, but it's moot since already internal inconsistency of SM has been demonstrated.

Perform the same evaluation for Yilmaz metric, and by simple inspection, actual spatial metric isotropy guarantees the same depressed value of interior spatial metric, throughout the entire hollow interior region as at the shell surface. Just as for clock rates. (Sans an obvious small and smooth change within the notionally very thin shell wall.)

Which appears entirely consistent with Mach's principle and suggests looking at gravity as fundamentally an inertial field and it's spatial derivatives.

4: Claims to the effect at least some of the above arguments are moot, because one can cast the standard anisotropic form of SM into a supposedly physically equivalent ISM (isotropic SM) form, has been shown to be incorrect in post
viewtopic.php?p=864#p864 (sans corrected expression for g_rr next post on).
SM and ISM are not physically equivalent. SM is non-Euclidean intensively, whereas ISM, like Yilmaz metric, is Euclidean in the differential limit as dr' -> 0.
One needs to compare SM, not a pseudo-equivalent ISM, to genuinely isotropic Yilmaz metric.

Again, anyone feel free to hop in and point out any substantive errors here.

[kev01]

Too late once logged out to edit so....
Apologies, but itemized 1: last post contains an obvious issue - the Yilmaz expression for g_tt I used 'blows up' as r -> 0, whereas the 'equivalent' SM expression goes to zero at r = r_s.
Maybe confusion owing to not tracking for sign of Newtonian potential vs expressions not using it.
In terms of equivalent coordinate time dilation (as frequency redshift):

SM: dτ/dt = √(1-2GM/(rc^2))
Yilmaz: dτ/dt = exp(-GM/(rc^2))

Hope that's it!

[kev01]

Does anyone else - the OP seems to have fled his own thread - have a useful input to make on what I have claimed above? It's not a trivial claim.
The substance of which, notwithstanding trivial errors belatedly corrected, should be easy to methodically shoot down.
Point-by-itemized-point, assuming each and every such point is fundamentally flawed in essence. Well?

PS: Constructive criticism rather than hostile 'you haven't rigorously proven anything' reactions appreciated.
My arguments are obviously broad-brush conceptual in nature.

[kev01]

Such a disappointment. Jay has clearly abandoned his own thread, with no explanation for not providing the courtesy of a reasoned response to my 'anti-GR' (to put it in the negative) 4-points argument favoring another theory, at least exhibiting a level of self-consistency unmatched by GR.
But it was explicitly made open to ANYONE to hop in and critique the essentials. Sure I made serial bloopers but none were of a conceptual kind.
I'm a self admitted amateur with no training in GR. That however may be a blessing not a curse.

Why after more than 700 views (many even allowing for bots/crawlers), has NO-ONE attempted a point-by-point rebuttal?
Meanwhile, FrediFizzx serial posts in the usual 'Bell was an idiot' type thread, but with no responses. Has this forum site become defunct?

[FrediFizzx]

... Has this forum site become defunct?

Yes and it only has 21 members. But I will keep blogging away on it.
.

[kev01]

... Has this forum site become defunct?

Yes and it only has 21 members. But I will keep blogging away on it.
.

Well Fred, having responded in some fashion at least, you have demonstrated this site is not totally defunct after all. Congrats!
Still, it would be nice if Jay or anyone else really, provided some useful thread topic related feedback to my input here. Or is it cyanide to challenge GR in any serious intent way? Seems so.

[kev01]

This situation of continued silence on a decidedly non-trivial attack on the Sacred Cow known as GR is bothersome to put it mildly.
Jay - if perchance you still subscribe to this forum and this thread in particular - do the decent thing and respond in some meaningful manner!
I can guess someone, a known irrationally motivated foe of mine, might have 'tapped you on the shoulder' and pointed you to my position on a certain non-physics related topic. With the perverse intent of somehow 'damaging' me as revenge. If that's the case, and it motivated you to avoid me like the plague, just come out and say so! Otherwise, please explain your reticence to rejoin the discussion here!