We argue that a black hole can be viewed as a gravitational optical element that images its interior onto the horizon. Being diffraction limited the Airy hyper-ball that forms as a result of interference of gravitational waves, does not allow for infinite resolution. Thereby effectively censoring the geodesics’ singularity at r --> 0. The mechanism proposed must imply intrinsic angular momentum as in the Kerr black hole solution. However, assuming that a static black hole develops from an initial Kerr solution the destroyed hyper-ball is delegated to the horizon by the principle of increasing entropy. This lost information about the system’s resolution is now packed on the horizon, which in effect provides the censorship.
>A central problem of the BH solution is its singularity. Unlike the chart
singularity of the Schwarzschild metric the Eddington-Finkelstein coordinates [A. S.
Eddington, Nature, 113, 192 (1924), D. Finkelstein, Phys. Rev., 110, 965 (1958)]
suggests a physical curvature singularity at r = 0, since 𝑅!"#$𝑅!"#$∝ M!/r! as r → 0.
For rigorous calculation a physical curvature singularity at r = 0, see
http://arxiv.org/abs/gr-qc/9707029
Einstein dismissed the possibility of black holes in 1939 due to the lack of time for their formation. Dirac did the same in 1962, writing that the region inside the Schwarzschild radius should not be taken into account in any physical theory for the same reason. I agree with Einstein and Dirac. Even Oppenheimer & Snyder conceded that a singularity cannot form in finite time. We can now point to quasars and gravitational waves as evidence that Einstein and Dirac understood gravity better than those currently ruling the roost. General relativity does forbid singularities, claims to the contrary are not a legitimate part of science.
Preprint Dispelling Black Hole Pathologies Through Theory and Observation
Preprint Coincident Down-chirps in GW150914 Betray the Absence of Eve...
Experiments to test Ferent Gravitation theory vs Einstein Gravitation theory!
In the double slit experiment the interacting observer is an instrument, detector…
My experiment (I can not do this experiment in Romania): if you replace the detector with a piece of metal the wave will collapse (in Einstein Gravitation theory the wave will not collapse, only travels through warped spacetime) into a particle because of my theory photon – graviton interaction:
Ferent equation for photon – graviton interaction:
E = h × f + a × f - a × ν
where - a × ν is the negative energy of the graviton
ν is the frequency of the graviton
Here we know the frequency of the photon f and the frequency of the graviton f. With different metals we have different frequencies of the graviton ν.
A lot of experiments can be done, and will result a lot of data!
Ferent gravitation theory explains the double slit experiment!
https://www.researchgate.net/publication/299135595_Ferent_Gravitation_theory
You can read on my theory:
Decoherence explained by my theory
The electromagnetic wave is the superposition of 3 sinusoids; this means the electromagnetic wave will be collapsed by the presence of an electric field, of a magnetic field, of a gravitational field, by another electromagnetic wave…
In my electromagnetic theory, gravity does collapse quantum superpositions, gravity bends light because light has 3 sinusoids, has a gravitational sinusoid!
In Maxwell electromagnetic theory, gravity does not collapse quantum superpositions, gravity does not bend light, because light has only 2 sinusoids!
So decoherence is due to the gravitational field, for example to the gravitational waves generated by the observer in the double-slit experiment.
Article Ferent Gravitation theory
I see no one has yet answered Thierry's objection to Robin's comment.
The Schwarzschild solution supposes as an hypothesis that there is a solution to the field equation which is (a) forever static and unchanging, and (b) existing in a universe by itself without any other objects (even at infinity).
Since the Schwarzschild metric is completely static, it can never "form". It has to have always existed exactly as it is. When we get into dynamic solutions to the field equation, all the objections of Robin and the luminous names he cites are valid.
Secondly, since the Schwarzschild metric is solitary, in a universe by itself, neither we nor anyone else can ever observe it, and therefore it is possibly not a good description of massive gravitational objects that we do observe.
Now that we have gravitational wave evidence for "merging black holes," a better explanation than just "trust the numerical relativists" should be developed, because Schwarzschild is the only widely known formulation and it just is inadequate with which to think about merging objects.
I don't think GR is wrong just because there is no competence to solve its dynamic version. The solution would be even better with perturbative scaling. Always we must think about what is the theory, what is the area of validity and what is the approximation.
The energy-momentum tensor of a black hole, or what curves the Schwarzschild geometry?
Using distributional techniques we calculate the energy-momentum tensor of the Schwarzschild geometry. It turns out to be a well defined tensor distribution concentrated on the r=0 region which is usually excluded from spacetime. This provides a physical interpretation for the curvature of this geometry.
http://iopscience.iop.org/article/10.1088/0264-9381/10/11/010/meta
Thierry, no one (that I know) thinks the universe cannot form. A few people think black holes cannot form, but that opinion (which I once shared but no more) is based on the static analytical Schwarzschild solution.
To be precise, Schwarzschild-related solutions are the only well known analytical solutions that pertain to black holes. There are two other classes of solutions. One is the Robertson-Walker cosmological solutions, which are dynamic. But the important ones in use today are the numerical solutions, for which we have no analytical equivalent. Therefore it is difficult to discuss them. That's what I meant by saying we need some option better than to just trust the numerical relativists. At least, we need some quasi-analytical insight into their solutions.
Robert, did I read you right? If so, what was it that caused you to embrace the dark side - do you find the paradoxes alluring?
Robin, actually I should have said I've moved to the position of being unsure. It was primarily Klaus Kassner who persuaded me that there might be a flaw in thinking an object could not cross an event horizon in observer time. Another fact is that about a year ago I realized that the proper distance to an event horizon is not infinite, even though the radial ds does become infinitesimal. If I integrate the trajectory of an infinitesimal test mass in observer units, at NON-relativistic velocities, I'm pretty confident the infinite slowing of velocity along with time prevents crossing the event horizon. However, in reality velocity becomes relativistic. The same thing may still be true. but the integral is a bit difficult and I haven't worked it out.
Kassner's main point is that the fading, slowing signal from an infalling object emitting a signal is not a continuing signal, but an infinite slowing of the final signal transmitted. He claimed that if the infaller were transmitting time tags, there would be a final tag and none beyond that. He promised to write a paper on it, and I'm just witholding judgment until I see his paper.
Thierry, I am not qualified to argue details of the FLRW metric. In reviewing two articles on its derivation, no one seems to explicitly start with Schwarzschild.
https://en.wikipedia.org/wiki/Friedmann%E2%80%93Lema%C3%AEtre%E2%80%93Robertson%E2%80%93Walker_metric
http://www2.warwick.ac.uk/fac/sci/physics/current/teach/module_home/px436/notes/lecture20.pdf
Since it assumes isotropy, there will be a certain limited symmetry to the also isotropic (spherically) Schwarzschild metric. But it assumes homogeneity, which is vastly different than Schwarzschild, and of course also variation with time.
Hi Robert, thanks for taking the trouble to explain your latest thinking. I agree that the integrated distance to the horizon is finite. I also take your point about infinitesimals. Einstein appreciated that time halts at the horizon relative to all external clocks but there was still the theoretical possibility a particle could reach the horizon before the universe becomes infinitely old. In fact, calculations back up Einstein's stance, as I'm sure he was aware, particles really cannot get to the horizon without the infinite passage of integrated time elsewhere.
Kassner's argument is very familiar, emphasising the observational aspects and how photons from the infalling object rapidly stop escaping. It originated with Misner, Thorne and Wheeler but in "Gravitation" they were merely pointing out that it makes no difference from an observational point of view whether the black hole actually forms or not, whilst acknowledging the fact that the event horizon cannot really absorb anything in finite external time. Kassner and others now this argument to distract and confuse people but it can be easily demolished.
But let me first point out that MTW's "excellent approximation" can go horribly wrong. If event horizons cannot form then there is nothing to prevent collapsed objects from assuming a toroidal topology supported by rotation. This then allows the objects to accrue a significant electrical charge, a net charge that can be very well-defended by a self-generated poloidal magnetic field. This can account for the properties of quasars (beamed relativistic jets of charged particles, intense energetics and curiously short lifespans) far better than electrically neutral Kerr black hole models.
So back to the misleading argument, which is a bit like a magician's sleight of hand: watch what's going on over here and you will hopefully forget about what's happening over there. True, the emitted photons do get redshifted and become scarce, and it takes them an increasingly long time to climb out from ever closer to the event horizon, but a very long time is still short compared to infinity - which really is how long the infalling object needs to reach the horizon. The key thing to remember here is that no matter how long the observer waits, he always has the option of scooping up a timelike infalling particle before it gets to the horizon. This is very easily proven by the mathematics. As for a photon aimed at the event horizon, you can slide a mirror in between the horizon and the photon at arbitrarily late times so that it is reflected back out again. Therefore, particles cannot be absorbed, even if they get extremely close to the event horizon. Kassner's little story is just a smokescreen. Since an event horizon cannot capture matter in a universe of finite age, it is safe to conclude that black holes simply cannot form.
Another common (but incorrect) argument is that nothing can prevent time from advancing for an infalling object whereas infinite time dilation is perfectly capable of doing that. It helps to think about what the infalling astronaut experiences. Kassner might say he will cross the event horizon as his watch reads 10pm and he will hit the event horizon at, say, 10:01. In fact, for this hypothetical scenario the astronaut can stare at the watch but as the time approaches 10pm the second hand will abruptly halt. The astronuat, however, will not be aware that the second hand has halted because his mind will also suddenly freeze and cease to function at the same moment.
If this seems absurd it is only because the starting assumption, that we have a black hole within our universe, is absurd. Einstein could appreciate this, and so could Dirac:
There is no need censor a Black Hole singularity, since singularity itself doesn`t exist. Singularity indicates a flaw in the theorem. Penrose and Hawking singularity theorems pre-assumed a flat universe. Unfortionately the actual spacetime of the universe is globally hyperbolic. The hyperbolic structure prevents singulatity to be formed. The nature is perfect.
Chapter Nonsingular Black Holes
In Gravitation, section 33.1, MTW conceded that gravitational collapse does not literally produce a black hole, but they tainted that admission by appending a misleading statement - one that many people who should know better now swear by:
For all practical purposes the phrase "black hole" is an excellent description. The alternative phrases "frozen star" and "collapsed star" emphasize an optical-illusion aspect of the phenomenon.
the Airy hyper-ball concept seems to bare relation to the Penrose trapped surface which to my understanding both D. Bar (see link below) and D. Christodoulou associate with gravitational waves (“The Formation of Black Holes in General Relativity”, EMS Monographs in Mathematics, January 2009). D. Bar also considers the Gravitational holography as a result of GW.
http://arxiv.org/pdf/gr-qc/0605115v2.pdf
Gravitational Radiation: A New Window onto the Universe by Kip S. Thorne; draft of 16
September 1989 — copyright 1989 by Kip S. Thorne
Near the focal point of a gravitational lens, the radii of curvature of the wave fronts are no longer huge compared to the waves’ reduced wavelength. As a result, the waves cease to propagate along null rays and begin to diffract, thereby lessening the strength of the focusing. The analysis of this is no different for gravitational waves than for electromagnetic or scalar waves, since polarization plays no important role. The analysis can be carried out using the flat-spacetime wave equation hαβ = 0 in a nearly Lorentz frame of the focal region. One switches from geometric optics to this wave equation as the waves
near the focal point. Then, once the waves are well past the focal point, one can return to geometric optics. One thereby finds that diffraction almost completely wipes out the effects of gravitational focusing, unless the waves’ reduced wavelength ̄λ is small compared to the lens’s gravitational radius 2GM/c2 = 3 km(M/M). (Here M is the lens’s mass.) This criterion applies whether the lens is a black hole, or a star like the sun, or a galaxy.
For an order of magnitude discussion see, e.g., Sec. 2.6.1 of Thorne (1983); for full details see Bontz and Haugan (1981)
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