The first to ask a question from my question, - why are there no takers yet for a logical discussion on GTR?

Cosmic speed limit is one-third the speed of light for sizable particles as proved by me.. My view or according to my revised view of special theory of relatiivty, there can exist particles like ghost particles( whose square of mass is negative), are part of space_time , what we associate as dark matter.They can travel upto 500000km/s and exceed the speed of light. Hence they can escape the event horizon. Hence, for these particles apparenthorizon is of only anything to be reckoned

Dear Andrew Worsley

Black holes are fascinating objects. The gravitational force of black holes is so intense that it can generate, according to GR, effects and events that stir our imagination, and raise questions that transcend physics and philosophy. The attractive force of a black hole can, as you say, stop time, turn space inside out, establishing what is known as a point of no return.

GR, on the other hand, allows us to explore, among other things, the limits of the universe and the nature of time and space. It is important to remember, however, that GR is a classical theory. Although GR has undeniable success in describing many physical phenomena, GR encounters some limitations in the high energy / strong gravity region.

Despite of that, with GW150914, the first direct gravitational-wave detection, LIGO got an unprecedented view of strong, rapidly changing gravity in action in our Universe. That was the first time LIGO has been able to observe gravitational waves to test our current best theory of gravity: Einstein's theory of General Relativity.

See (www.ligo.org/science/PublicationGW150914TestingGR/flyer.pdf).

According to GR, in the “center” of a black hole, its gravitational singularity corresponds to a one-dimensional point which a mass content located in an infinitely small space, the corresponding density and gravity become infinite and space-time curves infinitely. In this limit, the laws of physics, as we know, are meaningfulness. Kip Thorne called this point as “the point where all laws of physics break down".

Physicists believe that these predictions demonstrate that GR has reached its limit of validity at this point, making it necessary another formulation to overcome these limitations by extending GR to the boundaries of the non-return point. One of the expectations is that at this limit, in view of the physical scales then present, quantum gravity quantization effects become important and may be able to describe black holes without the need for singularities.

There is also a hypothesis (the "cosmic censorship"), indicating that the black hole's singularity remains hidden behind its event horizon, in that it is always surrounded by an area which does not allow light to escape, and therefore cannot be directly observed.

And there are scientists looking for evidence, tests, about the geometry of the event horizon in Black Holes. See for instance: Does the black hole shadow probe the event horizon geometry? Pedro V.P. Cunha, Carlos A. R. Herdeiro, Maria J. Rodriguez.

(https://arxiv.org/pdf/1802.02675.pdf)

Your question is about logic. Although formal logic is an essential element for the progress of science, in this field of activity (as well as in QM and QFT) I prefer to think in the context of Hegel's conception of dialectical logic. We continue the discussion another time. Best regards.

@Cesar

Good and open minded answer.

I agree GTR has reached its limits.

Yes the Wheeler Thorne Misner approach is a step forward from general relativity. So at least the singularity is not at the event horizon and the black hole can have a radius and a volume.

But we still have the problem of the singularity. And we are no closer to quantum gravity.

Gravity waves don't prove GTR, they rather strongly suggest the existance of gravitons though. And there remains a question, why is there a bifurcation in the 3 BH mergers but not in the neutron star merger.

Dear Andrew

Sorry but of course GWs are a great achievement of GR! Our knowledge about GWs is based strictly on GR predictions.

How we interpret the question depends partly on how far we believe that apparent, visually-observed effects should define reality.

Under GR1916, time appears to stop at the horizon as seen by a stationary distant observer, and that same horizon ought to exist for the set of all observers outside the hole who are stationary wrt the hole (those closest to the horizon experiencing arbitrarily-great gee-forces to stop them being dragged in). Under GR1916 we interpret this as meaning that events below the r=2m horizon are causally disconnected from the outside world.

However, this identification of "seen" and "deduced" reality doesn't always appear in other theories. Under a Newtonian-based "dark star" description, we still have the same apparent clock-stopping at r=2m as seen by a distant observer, but this is considered to be merely a projective artefact – a particle can enter a dark star and later be thrown free, and will subsequently be seen to exist in two places at once – we'll see the more aged escaped particle as well as the remnants of its earlier image still permanently frozen into the horizon. The fact that the image appears forever to be approaching r=2m but never actually reaching it, with its timeflow apparently slowing towards zero coexists with our knowing for a fact that the particle really did continue ageing, did enter and escape the horizon, and now exists in our detector.

While GR1916 inherits some of the "what you see is what there is" philosophical approach from special relativity, it allows a body briefly moving behind a gravity-source to appear to split into multiple objects and then re-coalesce again due to lensing effects, so what we see under GR isn't always considered to be entirely literally real.

The 1916 theory has a problem with observers moving wrt a horizon – if you let yourself fall into a black hole, you should be able to see events generated below the horizon – you just shouldn't be allowed to communicate them back to the outside world. That might appear to be consistent, but there's also an apparent paradox regarding horizon positions associated with relative motion. If motion shifts and gravitational shifts both obey the SR relationship, then one might expect all observers to agree about the position of a horizon (similar to how all observers under SR agree that a given lightbeam has the same speed). It's a velocity-addition thing, under SR, c plus any velocity gives c.

However, a moving black hole cannot show the same effective horizon to everyone. If a horizon is defined as the set of points where a lightray aimed at the observer is frozen and neither approaches them or recedes from them, then if light emitted at r=2M remains frozen into the r=2m surface, and this surface recedes from the observer, then by definition, those rays are now moving away from that observer. So there must be another intermediate "effective" horizon further out, somewhere between r=2m and the observer's position. Which means that events hidden behind an effective horizon for one external observer can be visible to another, while those two observers are in two-way communication.

Working Paper When a black hole moves: The incompatibility between gravita...

This means that the GR1916 idea that horizons have to be absolute and agreed is geometrically unworkable. Black holes have to show more sophisticated observer-dependent horizon behaviour.

Happily, this seems to generate an indirect-radiation effect that seems to be a classical analogue of Hawking radiation under QM.

Unhappily, this physical behaviour doesn't seem to be compatible with the current SR-based general theory.

So general relativity appears to be geometrically inconsistent and overdue for a rewrite.

AW: " Gravity waves don't prove GTR, ... "

CZV: " Sorry but of course GWs are a great achievement of GR! Our knowledge about GWs is based strictly on GR predictions. "

Actually, gravity-wave behaviour is one of the 1916 theory's weak points.

Gravity-wave propagation is desperately nonlinear, it involves a wave propagating at the velocity of light, that itself represents a change in the velocity of light. The geometry that describes such a situation is an acoustic metric.

Acoustic metrics didn't start to be properly studied as a mainstream subject until the 1990s. People were interested in them as "toy models" for the behaviour of a potential future theory of quantum gravity, because they generate classical trans-horizon information leakage that corresponds statistically to the behaviour of Hawking radiation under quantum mechanics, in a way that can't be replicated classically under the current 1916-based system.

Acoustic metric-based relativity is the main competition to the current Minkowski-metric-plus-gravity system that makes up current GR. Since gravitational waves HAVE to show acoustic metric behaviour (as do cosmological horizons, which fluctuate and radiate in response to events behind the horizon), acoustic metric principles aren't avoidable, and seem to be more fundamental than the current system.

Gravitational wave propagation was never properly modelled by GR1916, and couldn't be without bringing down the whole theory, because acoustic metrics require non-SR relationships, and Einstein's general theory specified SR's equations as a foundation.

So if anything, gravity-wave modelling is another inconsistency in Einstein's 1916 theory that points towards the theory's downfall.

AW: Why does GTR break down at the event horizon?

It doesn't, only the Schwarzschild coordinate system breaks down there. For alternatives, see this article and the links in the "see also" section:

https://en.wikipedia.org/wiki/Kruskal%E2%80%93Szekeres_coordinates

EB: Gravity-wave propagation .. involves a wave propagating at the velocity of light, that itself represents a change in the velocity of light.

For a "+" wave propagating in the z direction, when the speed in the x direction is increased, that in the y direction is decreased but the speed in the z direction is not affected.

EB: .. the current Minkowski-metric-plus-gravity system that makes up current GR.

That is not the nature of GR at all.

Hi George

This is an interesting point of view. Using the Kruskal–Szekeres coordinate system to describe the Schwarzschild geometry for a black hole the new coordinates will cover the entire spacetime manifold of the maximally extended Schwarzschild solution and GRT becomes from the math point of view well-behaved outside the physical singularity.

Yes, it's well known that the singularity at the event horizon is a coordinate artefact only.

Hi George

I have the same opinion. I am working also on a alternative approach to the big bang singularity. Thanks for the hint.

Paradoxes of a fallen theory, but it is being kept because it is a well done fit to Newtonian gravity theory.

• Nobody has observed a 'black hole'
• Time and length seem to change, but the rate of their seemingly change depends on the speed of used light beam, see

  Data 111 years of Magic are enough: Let us return to Science now

• General relativity cannot solve neither a single two body problem, see https://www.researchgate.net/post/Can_somebody_solve_the_next_problem_by_using_only_general_relativity
• All supposed successes can be easily explained by alternative views, RG has a plethora of such presentations

dear all

The problem of singularity that is mentioned in the question is not just a mathematical fault that can be easily solved using some mathematical tricks. The problem is deeper and it is one of the heavy stones in front of unification between QM and GR.

The answer of the above question is simply the GR solutions does not give the complete picture of what is really happening to the space time near the very heavy objects. It really needs modifications and the solutions need to be developed, however the starting point I suggest is from the SR not from GR, because the modification should start from the SR, which also does not give the complete picture. We are dealing with physics that is more than 100 years old, with no essential modification in spite of the closed road towards unification, which Einstein himself had already admitted it before 50 years. Do we need another Einstein to tell us that this road is closed and we should try other ones including modification of the GR and SR themselves.

“….Time stops at the event horizon so nothing can fall into a black hole in the lifetime of the Universe in GTR…”, etc.

Nothing happens with the time everywhere in Matter, including “at the event horizons”, and all what have corresponding motion’s parameters without any problems and rather quickly fall “into a black holes” ;

which don’t exist, of course, since Matter’s spacetime is the absolute [5]4D Euclidian empty container, where material objects and the system “Matter” as a whole, exist and uninterruptedly change; there cannot be some holes in this emptiness, it is a very big hole itself.

Though indeed a very massive and compact material bodies can have and seems have some unusual, comparing with macro-bodies, properties.

As well as the GTR breaks down in the reality not because of the thread’s reason, but just because of it is based on evidently wrong postulates and so predicts a lot of rather “strange” things, including “black/white/ worm… holes”, “ripples of the spacetime”, “bobbles in the spacetime”, “foams in the spacetime”, etc.,etc., etc.

When the real theory of the gravity will be the theory of the 4-th Natural fundamental force “Gravity”, which in a number of properties is similar to the other, i.e. Natural fundamental EM force.

Besides see https://www.researchgate.net/publication/265509276_The_informational_model_-_gravity

https://www.researchgate.net/publication/277710038_The_informational_model_-_gravity_a_next_experiment,

and https://www.researchgate.net/publication/273777630_The_Informational_Conception_and_Basic_Physics

Cheers

.

@Cesar

Show me exactly how GTR predicts gravity waves and I wiil agree with you.

@ERic

Good observations, it is important that people do no follow the flock and just assume without question.

Well it is very simple. Will show...

Hi

I show you the complete development as presented in my favourite text book when I was a student (long time ago): Adler, Bazin and Schiffer.

1. They start from the linearized equation for the perturbation term of the metric tensor (they write the metric tensor as the flat-space Lorentz metric tensor plus a perturbation term Gamma_mu_nu (see Weyl solution)) - see below.

2. In the following they show that the Riemann tensor which gives an absolut criterion for the existence of a gravitational field, itself obeys the wave function. See photo

3. Plane wave solutions imply that the Riemann tensor is highly degenerate - see below

4. The only non zero solutions are canonical-wave solutions - see below

5. Solutions

6. Analysis of nature of GW waves.

I show the cover of the mentioned book as well as a book I had the honour to be the Editor in which Abbot et al published an article about LIGO disvovery of GWs that gave the Nobel Prize to the main eesearchers of the project.

I am talking about Weiss, Thorne and Barish, Nobel Prize 2017.

The results I show are the predictions of GR so many years ago on the existence of GWs. And the basis of LIGO experiments...

Thank you Cesar

I am impressed

A flat space Lorentz metric, is however only an approximation. So it is the approximation that predicts gravitational waves.

Δφ ≈ tanΔφ = 6π m2 (4)

L2

where m = GM/c2, and a(1-e2) = L2/m, G is the gravitational constant and c is the speed of light, a is the semi-major axis and e is the eccentricity., T is the time of revolution in seconds, є is the amount of the rotation of the orbital ellipse [1].

and it is the approximation tanΔφ , that is more correct than GTR because the approximnation takes into account the fact that we are dealing with straight line geodesics, not curvature. And it obviates all that metric tensor nonsense. And it obviates all those silly infinities, and it also explains the gravity of dark matter, and much much more .

Touchee

About the gravitational waves see also the SS post in

https://www.researchgate.net/post/Does_the_gravitational_wave_detection_is_real

Cheers

Dear Andrew

I am talking about a prediction of GW based on a geometric Lorentz invariant description of the Universe not about a parametrization of GW. So, I cannot follow your argumentation. I am talking about a theory that preserves conservation law, symmetries, Lorentz invariance and so many other fundamental aspects on physics. Sorry, and don't take this statement from a personal level, I have no clue what are you talking about,

Thanks Cesar,

I do not take offence, but rather ask the question have you ever been able to do a single calculation to accuratley solve using full GTR, say the advance in the perihelion of mercury without a supercomputer, and how long did that take?

Hi Andrew

You do not need a supercomputer to do such calculation...

@Cesar ,

Which means, no you have never performed an exact solution, apart from the Schwarzschild radius.

Otherwise you are talking about approximations.

Show me an exact calculation, lets say for the advance in the perihelion of mercury.

The only exact solutions that were available initially were the Schwarzschild radius and a few others. And the Schwarzschild radius assumes a static black hole which is a perfect sphere, (when we know that black holes like other bodies rotate).

In other cases you do need supercomputer, and there are a lot of assumptions built into these programs that do numerical realtivity.

I think you are collectively fooling yourselves.

Hi, of course depends on the degree of precision you want ... there is no such thing "exact solution" in most interesting problems in physics...Einstein did his calculation (of course it was an approximation) without computers, supercomputers, etc...

@Cesar

Thankyou for agreeing,

But the point is the maths is so arcane that it does not allow you to obtain an accurate answer without using some sort of approximation - even when you do use a supercomputer.

Hi yes. I can give you an example. Today I work in nuclear astrophysics and general relativity. But I used to give in the past an example to my students of nuclear physics. It is related to the wave function of U238. In order to antisimetrize the wave function of U238, you have to apply the antisimetrization operator "A" which has, IF YOU DO NOT USE ANY APPROXIMATION, 238! terms, i.e., the factorial of 238. If you calculate observables associated to U238 you have to consider 238! times 238! terms

Do you have any idea of how huge is this number? If you do it by hand you would need "several lifes" to finish it...

Hi Cesar,

Valid point.

And here we come full circle, that is what the equation below does -obviates the repetition that is required with delta theta, for tan delta theta is the correct derivation, because it is a geodesic - and has no recurrent terms. Whereas in delta theta the corrections required for the curvature of space-time are infinite

A flat space Lorentz metric, is only an approximation, which requires the correction

Δφ ≈ tanΔφ = 6π m2/L2

where m = GM/c2, and a(1-e2) = L2/m, G is the gravitational constant and c is the speed of light, a is the semi-major axis and e is the eccentricity., T is the time of revolution in seconds, є is the amount of the rotation of the orbital ellipse [1].

Let the logic see the equation.