Following references are useful in this context

Thanks Biswajoy,

Can you give me a synopsis of what Hawking is saying

@ Ales

When you say GR says gravity escaped the EH, can you explain/give  references

Many thanks

Perhaps it is time to open up the discussion a little.

By definition nothing can escape the black hole singularity, not even photons going at the speed of light. So the question remains how can the effects of gravity escape the black hole?

That is, how can gravity escape the black hole, particularly if we take the Wheeler Misner Thorne interpretation where the singularity resides within the black hole EH.

The most logical answer would be that the effects of gravity ( whether it be gravitons or some thing else) are travelling faster than the speed of light.

Well, maybe thats because Gravitiy is not transported by a particle like a "Graviton" but is in fact, like the classical definition of Einstein, a field. Like electric force has an electric field, which is part of space. gravity instead has an own field, and this field is space itself.  there is no such thing as a gravity "force". 

@ alexander.

But surely the EM force is  is due to EM radiation, transmitted by photons, or perhaps virtual photons if you believe in that QED .stuff .  So gravity should have some mediator

@ Remi

With the greatest of respect

With logic in mind,  a  static field does not conventionally explain the gravity around the Sun and its interaction with for example Jupiter, never mind black hole. Nor even the results of LIGO with the merging of two black holes- with enormous energy release.

Hi Andrew!

   In a "simple" geometrical theory one doesn't have to worry about how the hole's gravity "gets out" - when we interact with the hole, we're interacting with its external field, and/or its external curvature, which can be considered as having been "set" at the moment when the original body retreated inside the r=2M horizon.

From that moment onwards, the intensity of the field, and/or the shape of spacetime emerging from r=2M can be considered "locked" into the horizon. If no signals emitted within r=2M can escape, then nothing that happens within r=2M can change that external field or external curvature – to the distant observer, the apparent physics at r=2M remains frozen into the configuration that it had at the moment that the hole formed.

We could also try taking an "observerspace" viewpoint – visually, all the matter that ever fell through the horizon still appears to us to be frozen, as a vanishingly thin film of matter, vanishingly close to the horizon surface ... so from an observerspace point of view, one could argue that the field that we feel corresponds to the matter that we see, apparently //at// r=2m rather than inside it. The "deliberate naivete" of observerspace arguments doesn't always give foolproof results, but the approach sometimes works surprisingly well.

In a more sophisticated theory, things aren't quite so simple, and some sorts of signals //can// penetrate the horizon from within, which seems to mesh well with QM's Hawking radiation effect, so the "simple" explanation might not be correct, and GR might actually have serious problems regarding horizons ... but the question of "how gravity gets out" isn't really one of them. If you really need gravity to be explained in terms of messenger particles, you can have them being generated by the external curvature.

@ Eric

Yes all very conventional, but is it logical? After all, the black hole at the center of the galaxxy once it is formed then grows into a supermassive black hole. It is not static not fixed and continues to interact dynamically the the galaxy.

What you have been taught (indoctrinated) needs to be questiponed form time to time.

One question which affects your question is: Why does Gravity not interact with particles in the double-slit experiment? We know if particles interact with something (some call it "when the observer measures it") the wave-function collapses. So we try to isolate everything to get the wave function of particles. BUT: On Earth you can't just isolate gravity. So if gravity is transmitted by something, as you claim, why doesn't it lead to the collapse of the wave function like other interactions? Because there is no interaction, it's not a force transmitted by particles, but space itself and particle spread in space. Of course its just an idea, i'm not specialized in this field. 

@Andrew, Here is a summary of just the absolute basics.

According to Quantum Field Theory there is a classical vacuum and there are quantum mechanical fluctuations around the vacuum. Particle anti-particle pairs are created and destroyed. If a particle (antiparticle) is created with energy E then the corresponding antiparticle (particle) has  energy -E. These pairs obey time-energy uncertainty relation and thus live for a very short time. Now black hole is a classical object but it lives in space-time and so, just outside the radius r=2M, vacuum fluctuations do take place. The negative energy particle (antiparticle) falls under the gravitational influence of the black hole; it disappears inside. The positive energy antiparticle (particle) may or may not escape.  If it does it forms a radiation, called the Hawking radiation. This radiation has the character of a black-body spectrum of temperature inversely proportional to black-hole mass (T=10-7 (Msolar / M) Kelvin). Therefore, Hawking radiation is produced just outside the event horizon of the black-hole. However, the particle which goes in carries negative energy inside the black hole, therefore a black-hole does not live forever (evaporates).

As far as I understand, Hawking radiation is an interesting phenomenon because it provides a "missing link" between the physics of general relativity and that of quantum field theory.

@ Bisajoy

I am aware of the theoretical baiscs, but Hawking radiation wiil only extinguish very small black holes. By defintion those need to be primordial, because both stellar and supemassive black holes are too big and wiil not have had time to evapoarat in the way Hawing described in the current lifetime of the Universe

Besides nobody has observed Hawknig radiation.

Additionally the information from LIGO tells us that 3 solar masses were radiated away due the black hole merger. SO hawking radiation isn't the only way a black hole can realese energy

@ REMi

Your answer does not  tell us why the equivalent of 3 swolar masses was radiated away by the merger of 2 black holes observed by LIGO,

No schwarzschild metric has that much energy

" Yes all very conventional, but is it logical? "

Hi Andrew!

   Yes, it's logical. Perhaps not the whole story, and not necessarily the only possible explanation, but logically arguable.

When a black hole grows by swallowing extra mass, we can go on to suggest that the signal corresponding to the mass-increase slides around the hole exterior outside the event horizon and forms a new event horizon above the old one, centred on the new centre of gravity. It can be done with external curvature without having to probe the hole's innards and get a new signal out. When a black hole swallows another black hole, if the two original horizon diameters are d1 and d2, the diameter d3 of the resulting hole is d3=d1+d2, so the new horizon exactly encloses the two original horizons, along with a whole other volume of space alongside.

@ Remi

Exactly the point

The radiated energy must come  from somewhere, and 3 solar masses of energy is not insifignicant

The real explanation of this process is related to quantum tunnelling which is related to the treatment of matter in quantum mechanics as having properties of waves and particles. One interpretation of this duality involves the Heisenberg uncertainty principle, which defines a limit on how precisely the position and the momentum of a particle can be known at the same time. This implies that there are no solutions with a probability of exactly zero (or one), though a solution may approach infinity if, for example, the calculation for its position was taken as a probability of 1, the other, i.e. its speed, would have to be infinity. Hence, the probability of a given particle's existence on the opposite side of an intervening barrier is non-zero, and such particles will appear on the 'other' (a semantically difficult word in this instance) side with a relative frequency proportional to this probability.  Who want to understand how the uncertainty principle working in gravity, then review my explanation of light bending by gravity, Pioneer anomaly, Shapiro delay, and Mercury precession in my paper. In my paper there is no energy momentum problem. Infinities disappeared and no need to dark matter or dark energy. And who do not believe that, then I invite him to follow this RG

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

As it is written in this RG

For Planck's constant LIGO data of merging black holes has been suggested as a way to decide if the most extreme events can change the constant into a variable. So far the LIGO results have been used in modified PV theory at high speed to accept the possibility of invariant Planck's constant, without excluding the possibility of variation under extreme conditions within the limits of Heisenberg Uncertainty.

Constants will remain constants if we considered the uncertainty principle instead of the curved space-time in GR. In this case gravity is completely quantized!!!

http://www.ingentaconnect.com/contentone/pe/pe/2016/00000029/00000003/art00018

Dear Andrew,  

Purely in terms of general relativity, there is no problem here. The gravity doesn't have to get out of the black hole. General relativity is a local theory, which means that the field at a certain point in spacetime is determined entirely by things going on at places that can communicate with it at speeds less than or equal to c. If a star collapses into a black hole, the gravitational field outside the black hole may be calculated entirely from the properties of the star and its external gravitational field before it becomes a black hole. Just as the light registering late stages in my fall takes longer and longer to get out to you at a large distance, the gravitational consequences of events late in the star's collapse take longer and longer to ripple out to the world at large. In this sense the black hole is a kind of "frozen star": the gravitational field is a fossil field. The same is true of the electromagnetic field that a black hole may possess

This original idea by Matt McIrvin since 1995

Einstein believed black holes were impossible.

He was quite right to do so, because  the singularity threw up so many paradoxes.

So if you don't believe me, at least believe Einstein.

There is no apparent logical interpretation of the singularity.

If black holes were frozen stars it would be impossible for them to merge and emit 3 solar mass energy in gravitational waves - as LIGO has shown.

Stop tying yourselves in illogical knots.

In my theory there is no space-time continuum. Space is invariant and it is only time which is related to time dilation. The escape velocity locally at the quantum Schwarzschild radius is c the speed of light in vacuum, because all the rest mass will change to photons according to E=m0c2=hv0. But globally according to the time dilation c'=0 and that is related to the probability in this case which is equivalent to the probability equals to 0. But there are no solutions with a probability of exactly zero (or one), though a solution may approach infinity if, for example, the calculation for its position was taken as a probability of 1, the other, i.e. its speed, would have to be infinity. As we know the classical treatment of time is deeply intertwined with the Copenhagen interpretation of quantum mechanics, and, thus, with the conceptual foundations of quantum theory: all measurements of observables are made at certain instants of time and probabilities are only assigned to such measurements. In my theory radiation power is invariant across gravitational potentials. The energy of travelling quanta does not change from the source to the absorber in the RF of the emitter. Only the perceived frequency changes due to the gravitational time dilation, no radiant energy gets “stored” in the gravitational field while travelling.

As in this paper also http://arxiv.org/pdf/1404.4075v1.pdf

Calculating the ensuing travel times of light round the interferometer we find that the LT – due to its linear term x v/c2 – does not predict any Sagnac Effect, but results in c = const also in a rotating system as it does in an inertial system. This explains then why Ashby [6], e.g., uses the Newtonian or Galilean time transformation t’ = t rather than t’ = γ (t - x v/c2) when he calculates the Sagnac Effect in the GPS-System. This was also observed by Carroll Alley in a comment at the end of an engineering presentation on GPS and Relativity.  

In this case if we want to understand Sagnac effect by proposing time dilation in SRT, in this case we must understand what is the meaning t'=t0 at x'=x0 and t=t0 at x=x0. In this case we t=t'=t0 at x=x'=x0, and by considering the time dilation in this case, there must be two pictures for the moving train. These two picture must be separated in space and time, but entangled by the invariance of the energy-momentum four vectors.  In this case time dilation is resulted from the clock retardation. In this case the real transformation expressing about that must be vacuum energy dependent, and it is leading to the wave-particle duality and the uncertainty principle by the vacuum fluctuations. 

Now that is explained in my theory according to my transformation not LT, which is leading to explaining Sagnac effect exactly same as explaining Sagnac effect within the framework of the ether theory by instead of the Ether theory, it is vacuum energy dependent and in this case the uncertainty principle working by the vacuum fluctuations.

Dear Andrew,

Einstein not think that black holes were impossible, he thought that they were unobservable.

Dear All,

During the gravitational collapse or whatever formed the black hole, spacetime was being distorted and after the black hole formed spacetime retained the imposed distortion so nothing had to escape anything. It was like a dent in the fender of your car.

Geology and physics hmmm.

Yes he wrote a paper saying black holes could not exist in the 1930's because matter would need to exceed the speed of light to form a black hole. Look it up.

During the gravitational merger 3 solar masses in gravitational energy were emitted- Look it up.

P.S.

It is important that people stop making up the facts to suit their opinion. As Newton would say, when falsley accused of proposing gravitational action at a distance "Hypotheses non fingo"

Andrew,

Einstein's paper is mathematically correct, but he missed the point. (Actually, a student of GR should be able to reproduce his results as an exercise, with little help; originally I read only his abstract and got everything in agreement  with Einstein on two pages.) His spherical symmetric cluster model can only exist in a stationary state, if the radius of the cluster is larger than 3/2 times the Schwarzschild radius, otherwise the circular velocities of the stars at the outer boundary would exceed the speed of light. Einstein writes, that this is similar to Schwarzschild's result, according to which a static interior solution to his metric can only exist if the radius of the star is bigger than 9/8 times the Schwarzschild radius. (This belongs to a course on GR.)

But stars and clusters of stars can collapse and form black holes. It is a bit ironic, that this was completely clarified in the same year 1939 by Oppenheimer and Snyder in a classic paper, many students of GR know. All this is also clearly described in a non-technical version in Kiip Thorn's popular book on compact objects. It is somewhat ridiculous, that Einstein's paper is still cited by some people as a proof for the non-existence of black holes.

There are other occasions, when Einstein denied the existence of black holes

http://www.goodreads.com/trivia/show/224468-einstein-denied-multiple-times-the-exist

I am perplexed by this discussion that seems to be wandering about in a kind of never-never land. To form the black hole spacetime was warped and the warp was retained and deepened as the black hole evolved and it is the warping enclosing the black hole that produces the gravitational effects. Nothing has to escape the black hole to produce the gravitational effects around the black hole.

http://www.pbs.org/newshour/updates/hawking-meant-black-holes/

http://www.pbs.org/newshour/updates/hawking-meant-black-holes/

https://arxiv.org/pdf/1401.5761v1.pdf

Our present understanding of black hole horizons was reached only after Einstein's death, especially with Kruskal's paper "Maximal extension of Schwarzschild metric", Phys. Rev. 119, 1743 (1960). I remember its impact because I was then PhD student in Zürich. Before the situation was indeed confusing, but sometimes there is, fortunately, progress without Einstein.

@REMI

Good answer but i didn't and don't believe in virtual phtons as they are unecessary. Charges inetract with the vacuum by meann of the vacuum energy represent by the electric constant and the magnetic constant (previously known as the permittivity and permeability of free space). That is of course the same as dark energy but QM has simply overestimated  it.

Besides if vitual photons existed then it is quite likely that photons could emerge from the EH

Andrew,

If the Universe is created out of nothing, then a black hole is an agglomeration of bare positive charges (bare positive fermions). They are held together by magnetic potentials (A-vectors). Bare charge's compression generates magnetic potential perpendicular to the direction of compression. Notably, abstract charges (phi-field) and A-field are abstract quantities. Nothing is requited for their propagation. They influence distant objects instantaneously. Bare fermions do not experience Coulomb field. Bare charges generate bosons units (in the form of chains), ad infinitum and screen the phi-field strength. We observe magnetic potential only when they interact with charges. Magnetic potentials do not create boson units. However, they interact with the fermions in a boson unit and thus, make boson chains orbit the central black hole. These bosons are created by the abstract phi-fields. Massive a black hole is, stronger is its abstract phi-field (charge field). However, the net energy of the boson units generated by the phi-field continues to be zero due to their fractal growth (a boson unit is made of bare positive and negative fermion pair). Intrinsic spins of these bosons create gravity. Hence nothing has to come out of the black hole.

@Azizul

"If the Universe is created out of nothing" - stop right there.

That is a Big Assume, 

@Remi

E =hn 

where h is Planck's constant  and n is the number of quanta per unit time contained in a system, and also the frequency per unit time.  Specifically n =f.

If the quantum mass is h /c^2 per unit time, then the total mass is  m =hn/c^2.  

Thus  n = mc^2/h

Thus substituting n

Then E =mc^2 

Total energy E= hn is conserved hence the Big Bang arose form a cosmic black hole, Where the graviational dynamics where a black hole with in a black hole- 

The only supernatural intrevention was then  the creation of  a set of constants that were comaptible with life. 

Andrew,

This is a very pertinent question and I don't think anyone here has come close to providing a credible response.

I would add that it's not just gravity that supposedly escapes from these fantasy objects, so too does the electric field of any electrically charged particle captured in (impossibly) finite time through the (non-existent) event horizon - or so we are meant to believe.

Einstein and Maxwell were right. Black holes cannot form or capture matter in a universe of finite age - and nothing can travel faster than the speed of light, whatever the prevailing dogma may be. Notice that the only sensible solution to the information paradox is the one that gets no air time and the one that the (arrogantly ignored) architect of GR appreciated back in 1939: gravitational collapse is incapable of producing an object with an event horizon owing to the fact that gravitational time dilation grows without limit prior to the appearance of any horizon.

@ robin

Well you might say that the escape velocity c apllies and that doesn't produce an absolute black hole, and if so only at the inner (emitting) surface of the black hole. (I don't buy this zero volume stuff) But you still have gravitons emmitted from the emiiting surface so they must be tahyonic.

When you say the gravitons "must be tachyonic", do you mean that they must travel impossibly quickly and hence the assumption that black holes with event horizons exist and exert a gravitational influence on the rest of the universe must be false? If so, and gravity really is mediated by gravitons, then I agree. The same point of course carries over to the electric field which, we are confidently assured, is mediated by virtual photons.

If there are no gravitons then spacetime itself must superluminally propagate knowledge of the matter (and any electrical charges) hiding within the event horizon. The little snag here is that it rejects the fundamental basis of relativity theory. Fifty years of drivel, yet nobody is allowed to point it out. Meanwhile, the public are kept in the dark, and expected to keep funding this embarrassing "research".

Dear Andrew Worsley. you have made an excellent question…. I can make lot of others one:

https://www.researchgate.net/profile/Laszlo-Attila_Horvath/questions....

Please someone explain me: How was the distance of black holes determined? Their mass? How they can know that they will be able to use uncertain discoveries… Why Einstein did not discovered the gravity waves? because he has clear opportunity… To observe gravity waves we do not need LIGO tools!

best Regards LAH

P.S. These discoveries as they present deceptive!    The presentation has such a part witch are in contradiction with GR itself…

@ robin 

If Newtonian escape velocity is involved

We can do a quick calculation for the radius of that escape velocity for a black hole.

That is your answer 

Andrew,

I do not see any other assumptions are working. Any assumption we make, has to describe the present Universe as well. Zero energy Universe works perfectly well. Why should we abandon that?

The present Universe does not contain zero energy and is a lot bigger than most can imagine.  

Zero energy universe is pointless - like a broken pencil.

Dear Andrew,

·         Black hole paradox and ‘anomalous’ redshifts of compact celestial bodies are two of the many unanswered questions in the MTW model. Another, is that it holds on to the SRT concept of ‘constancy of c (speed of light)’, although between 1911-21, Einstein stated at four occasions  (quoted & referenced in our eighth Relativity paper mentioned below) about the‘General relativistic nature of c’ that relates to the variation in magnitude of c under the influence of gravitational field, that is, the variable nature of c in General Relativity Theory (GRT); the details and the reason for this deviation from Einstein have been pointed out from a comprehensive review of the Historical background that has been given in detail in our eighth Relativity paper titled “Evolved General Relativity Predicts ‘Sought-After Departure’ of STAR missionEvolved General Relativity Predicts ‘Sought-After Departure’ of STAR mission_v2”

Krishnan RS Mani

Your paper is similar of my paper in  http://www.ingentaconnect.com/contentone/pe/pe/2016/00000029/00000003/art00018

The difference I could Reinterpreted the SRT of Einstein according to the Copenhagen school and that means I could understand in my paper how the wave-particle duality and the uncertainty principle in micro world must work in macro world also.

I discovered that LT can't explain the motion well, and in this case there must be a new transformation must express about the wave-particle duality and the uncertainty principle. This transformation must be vacuum energy dependent and it is a transformation of acceleration by the vacuum fluctuations and by the vacuum fluctuations the uncertainty principle works. In this case time dilation is gauge theory and by the equivalence principle gravity is gauge theory. also According to that the reality is observer dependent not observer independent same in relativity of Einstein as he proposed. You can review my transformation 

x=R^2 (x'-vt') t=R^2(t'-vx'/c^2) y=Ry' z=Rz' and R is the Lorentz factor.

In this case light speed is locally constant and equals to light speed in vacuum, but globally it is variable and it is vacuum energy dependent, and in case of gravity it is gravitational potential energy dependent. No way to understand anything in physics without understanding how the wave-particle duality and the uncertainty principle must work in macro world.

http://www.ingentaconnect.com/contentone/pe/pe/2016/00000029/00000003/art00018

@ Krishnan/Azzam

I like your premise that light can theoretically travel faster than c. Indeed there is experimental evidence that shows this.

But that still doesn't obviate the difficulty where light is restricted form exiting the black hole, but gravitons it appears are not.

@Andrew,

In my theory, there is no graviton!! It is photon!! There is no travel faster than light locally. That is impossible in my theory.  But globally there is a possibility of measuring faster than c depending on the negativity of the vacuum energy when we considering x/t. That is  according to my theory because x is invariant and thus that related to time dilation, where  t' not equal to t which is gauge theory.  This is the reality of disappearing the twin Paradox in my theory. When the two twins meet at the same frame of reference, then one must be older than the other. Is that meaning the twin who is older than the other one was growing in a faster than light relative to the twin who is younger where the speed of light locally relative to the twin who is younger is the speed of light in vacuum c  in his reference frame, and also the speed of light in the reference frame relative to the twin who is older was c also locally. The answer there is no faster than light according to the invariance of the energy momentum. The energy is conserved and the information is conserved. Since in Einstein's relativity theory the global and local are independent, from that it is resulted the confusion in understanding how is the possibility of measuring faster than light globally, and in this case it is proposed the virtual particles and photons, while there are no virtual particles and photons. They are real, but we can't understand how they are real according to SRT.

Classically, the energy is universally defined in such a way that it is conserved as a result of the time-translational symmetry; and the action is defined in such a way that the condition δS=0 (stationarity of the action) is equivalent to the equations of motion. These are the general conditions that define the concepts in general and that make them important; particular formulae for the energy or action are just particular applications of the general rules.

 In quantum physics, the action doesn't pick the only allowed history; instead, one calculates the probability amplitudes as sums over all histories weighted by exp(iS/ℏ) which may be easily seen to reduce to the classical predictions in the classical limit. A stationary action of a history means that the nearby histories have a similar phase and they constructively interfere with each other, making the classically allowed history more important than others. And as we know, the classical treatment of time is deeply intertwined with the Copenhagen interpretation of quantum mechanics, and, thus, with the conceptual foundations of quantum theory: all measurements of observables are made at certain instants of time and probabilities are only assigned to such measurements.

In the standard theory, only particles cannot escape the event horizon, and gravity is not thought of as particles, but as a warping of space time; and that can exist at any distance (and already does, before the black hole is created, though the amount of warping decreases with distance according to almost exactly the 1/r-squared relationship of Newtonian physics). Any changes in the mass of the object or objects that become the black hole would change the warping of space time, and those changes are transmitted to distant parts of space at the speed of light by gravitational waves (or "gravitons", in the wave-particle version of the theory). How the gravitons are emitted depends on the theory used to describe their emission, as the contradictory theories above indicate; but changes in the warping of space are only detectable (sp?) outside the event horizon, so the gravitons/waves do not need to "escape" from the black hole to propagate to distant parts of the Universe.

/////

Additionally the information from LIGO tells us that 3 solar masses were radiated away due the black hole merger.

/////

I have an idea for above problem.

If a situation where R_gs’ becomes bigger than the minimum radius of the Kerr black hole occurs due to the particles(energy) absorbed form the outside, then it is possible for energy(and particles) to escape from the inside of the black hole.

R_gs’= The size in which gravitational self-energy becomes equal to rest mass energy.

I argue that,

We can solve the problem of singularity by separating the term of gravitational self-energy(sum of the gravitational potential energy) from mass and including it in the solutions of field equation.

*The concept of gravitational self-energy is the total of gravitational potential energy possessed by a certain object M itself. Since a certain object M itself is a binding state of infinitesimal mass dM, it involves the existence of gravitational potential energy among these dMs and is the value of adding up these.

In the generality of cases, the value of gravitational self-energy is small enough to be negligible, compared to mass energy mc^2. Therefore, in usual cases, |U_gs|

A large part of the reactions to the original question would presumably not have been written if the authors would have at least a rough qualitative idea of what relativists do when they solve (numerically) Einstein's field equations for black hole inspiral and coalescence. Below a few remarks on one of the treatments concerning horizons, which is conceptually transparent (although numerically not always the best).

Since no information can propagate from inside of the black hole to the outside, so that non of the exterior spacetime can possibly be affected by the black hole interior, it is sufficient to simulate numerically only the exterior of black holes. This approach is referred to as black hole excisions. Mathematical, no boundary conditions are required at the excision surface, since the so-called characteristics are directed inward.

Numerical, the implementation of this approach has some difficulties. I mention only one. It is usually not possible to locate in a numerical simulation the dynamically evolving event horizon, because this is a global concept. Therefore, the region inside the so-called apparent horizon is excised from the computational domain. In GR the apparent horizon is inside the event horizon or agrees with it (as for instance in the Schwarzschild case). The apparent horizon is determined by local equations (the expansion of certain outgoing null geodesics vanishes there).

Some final remarks. For the black hole coalescence one solves Einstein's vacuum equations, which contain no free parameters, but are highly nonlinear partial differential equation and the final evolution is extremely dynamic. The numerical results for the inspiring phase agree very well with analytic, so-called post-Newtonian approximations, but the entire evolution can only be computed with sophisticated numerical methods and modern computer power. The results of several independent groups agree. This is a tremendous achievement.

@ Norbert 

Thank you for your answer.

I have a question regarding your book "General Relativity with Applications to Astrophysics" 2004, page 360.

On page 360 you give  (Pb)obs - (Pb) gal   = - 0.174 x 10-12

where (Pb) gal  = 0.037 x 10-12.

This suggests that on its own (Pb)obs =     -0.137 x 10-12 

Is this correct?

@ Andrew

Yes, this is correct. This number is also given in table 5.2 on page 359. I checked whether there are more recent results for the system, but this is not the case, presumably because the distance to the pulsar can not be improved.

@Norbert 

Thank you very iintsrutve answer

The way gravitons leave the black hole is because gravitons interacts with themselves. A graviton leaving the black hole is pulled back, it generates another graviton farther from the singularity. It goes on until  a graviton leaves the event horizon, then it can be free.

There are obviously no limits for nonsense.

I can only say that everyone who imagine gravity needing signals from object that "gravitates" is hopeless with his/her gravitons.

You can think the gravity field is the same as the massive object - its mass field extends always to the whole universe, at least via spreading with the causal speed c from the event of the creation of the structural particles of it. No backreaction signals are principally needed. The mass distribution changes transmit signals too.

Only case when the backreaction signals can be remarkable is the matter gathering or collisions when the gravity "dig new deeper well" and the large previous gravity field must also change its form at very long distances. I'm just studying these kind of serial gravitational delays as origin of the dark mass problem.

None of these answers addresses why 3 solar masses were lost in gravitational energy

Why? Because the calculations give this. Less energy, but still a considerable amount is radiated already in the inspiral phase. During the time when the first order treatment is a good approximation, one finds an energy loss of about 10% of the reduced mass of the binary system. This is, for instance, derived in detail in the book "Gravitational Waves" by Michele Maggiore in Sect. 4.1 (completely accessible to students), Oxford University Press (2008).  This is really the result of Einstein's vacuum equations; no mystery!

@ Norbert.

The point being that conventionally nothing can escape the event horizon

And I don't believe that the space time is somehow "preset"  to give out this amount of energy.

So during the whole of the event the energy must come from somewhere. The question is where?

@ Andrew

The radiation produced during the inspiral phase is very analogous to the radiation loss generated in electrodynamics by two circulating charged particles and as a result approach each other. The latter problem is treated extensively, together with solved exercises, in Volume 2 of Landau-Lifschitz, Sect 70. Actually, for the early part of the binary black hole inspiral, when the leading contribution in a post-Newtonian expansion dominates, the treatment of the two systems is even mathematically very similar. In GR the problem becomes much more difficult when the separation of the two black holes becomes small, because of the high nonlinearities of Einstein's vacuum equations, but this is largely a technical difficulty (which has recently been overcome with the help of powerful computers plus analytical work). There is really no mystery. Just look up the calculations presented in text books.

Soon we will have many events and together with further interferometers we may be able to test GR in these extreme processes.

Gravitational effects are restricted by boundary conditions and physics interfaces.

Dear Andrew Worsley,

Onto base of a concept of gravity accepted by me, can be give response to your question… The Theory gravity forced by researchers of LIGO with their explanation is totally invented resolution… As they are making, contradict themselves. That is why such a lot question… Simply response to your question:

“By definition nothing can escape the black hole singularity, not even photons going at the speed of light. So the question remains how can the effects of gravity escape the black hole?“

Any physical changing in the stage of black holes are producing change in gravity field of black holes (information)… these are transmitted like (gravity waves) with speed like light!… Such a statement has a strongly question: why we did not discover the gravity waves before? Perhaps we were strongly blinded by… Best regards LA H

In GR the problem becomes much more difficult when the separation of the two black holes becomes small because of the high nonlinearities of Einstein's vacuum equations

But the uncertainty principle, the wave-particle duality solve the problem in a very simple way!!! In this case the energy is conserved and information is conserved!! But the question how the uncertainty principle and the wave-particle duality work in this case??? the uncertainty principle and the wave-particle duality keep on the linearity, because in this case space is invariant!!! 

This is very interesting paper.

http://www.scirp.org/journal/70953.html

@Norbert

Soon we will be very surprised

If somebody writes that "light speed is not a constant", he has not understood the foundations of GR. The extension of Maxwell's equations to GR was already given by Einstein and Grossmann in their famous "Entwurf " paper of 1913  (Collected Papers of AE, Vol.4, Doc13), and nothing has changed in this respect, since it is just based on the Equivalence Prinzipal (replace ordinary partial derivativer by covariant ones). Einstein presented these basic equations  in his part, Sect. 5, with the title (in my translation) "Influence of the gravitational field on physical processes , especially on electromagnetic phenomena". The equations are given under (23) and (24). Relativists know how to apply them correctly.

@Norbert

If someone writes in QED, that virtual photons can readlly exceed of  speed light - then that is standard.

Virtual photons are connected with Feynman propagators, and have nothing to do with real photons. One should know the subjects and not only words.

@ Norbert,

I am fully aware of the physics and I do not believe in the presence of virtual phtons in any case.

But that doesn't mean to stay that faster than light propagation within the black hole is not possible for gravitons.

And that specifically applies to gravitons and of course not light

@ Andrew

Wrong, gravitational waves  follow a wave equation with the standard wave operator. Consult in my book Sect. 5.1.1, in particular eq. (5.24).

Intriguing answer -of course gravitons follow the standard wave equation outside the black hole  event horizon (EH).

But is that an absolute within the black hole EH?

@ Issam 

Your speed is a coordinate speed, not the speed of light. In the geometric optic limit the light rays are null geodesics (see, for instance my book, Sect. 2.8), hence the square of the 4-velocity is  always equal to 0, as in SR (by the way of course also inside a black hole horizon).

The whole idea of the event horizon in GR is based on the constant speed of causality. Of course it must be valid inside the horizon too. Still, it's possible that there can't be any real event horizons in the observable spacetime as far as all the quantum effects considered. Maybe they are real or apparent or asymptotical, more research is needed.

@ Issam

In connection with your remarks concerning the speed of light in media the following fact is crucial (not so widely known), and has an interesting history.

In six letters to Wilhelm Wien from summer 1907, Einstein discussed the occurrence of velocities exceeding the speed of light (in vacuum) in dispersive and absorptive media and tried to answer the question whether such velocities are meaningful signal velocities, relativity forbids. Einstein's arguments were not really conclusive. As a result, Sommerfeld studied the problem in great detail, and proved in a remarkable paper that the front of a wave-signal can never exceed the speed of light in vacuum. Full details were published by him several years later (1912). Sommerfeld's definite analysis is well decided in Jackson's book on electrodynamics, Sect. 7.11: "Arrival of a Signal After Propagation Through a Dispersive Medium".

For a detailed description of the history see the Editorial Note in Volume 5 of the Collected Papers of AE, p.56: "Einstein on Superluminal Signal Velocities". This volume contains also his letters to Wien.

Since Maxwell's equations for media are Lorentz covariant (Minkowski), no additional problems arise for moving media.---  I hope this will help you.

Professor Norbert Straumann,

The local geometry of GR spacetime is flat or Minkowskian respecting any coordinate frame with invariant square line element ds^2, so locally and focusing and the radial motion ,the radial velocity dr/dt in Einstein universe is always equal to the speed of light c respecting any local (Minkowskian or flat) observer; in other words, c can be defined as the local (coordinate) speed of light and it is of the same value or constant in all local (coordinate)frames. 

Eureka!

@ Issam

Locally is the wrong word in this case. The tangent space has the geometry of Minkowski.

Dear Issam,

I agree with Hawking on the idea of event horizons being apparent and also I think it's all coordinate dependent. I had my thoughs far earlier than Hawking but not only because of quantum mechanics. The theory of GR seems to consist a interpretation that the gravity field don't changes its whole form at once with single signal of changed mass distribution but it can need serial of backreaction signalling. This kind of space-interaction prevent developing any real event horizons.

I find this whole discussion very nice.

My finding of c being a global constant in the equivalence principle is nevertheless worth pondering, or is it not?

Hi Otto

Good answer,

That light can go faster than light has already been experimentally established - without violating the "effect principle"

Hawking radiation!

Please check the link:

https://en.wikipedia.org/wiki/Hawking_radiation

This is a perfectly simple question with a very obvious answer: it cannot. If an object with an event horizon actually did exist, it would have no gravitational influence on the rest of the universe. Quite literally, it would not be part of this universe. The mathematics is absolutely clear: it literally takes forever for anything to reach (let alone cross) a BH event horizon, and this universe is not infinitely old. It immediately follows that gravitational collapse cannot produce an object with an event horizon.

Black holes suffer from numerous other pathologies and paradoxes - which so many theoretical physicists turn a blind eye to. The belief in black holes can be likened to a belief in fairies at the bottom of the garden. Einstein knew it. Lev Landau knew it. The designers of the Great Pyramid knew it - and still do. Hey, it's even possible that the Neanderthals knew it (but now I'm speculating). What is certain is that this galaxy has no need for a belligerent species that's hopeless when it comes to science.

I know the answer to the main question:

Nothing ever enters or even reaches the event horizon.

If c is a global constant of nature, as Zwicky first saw in 1929, confirmed eventually by Cryodynamics.

Gravitons interacts with gravitons, um graviton inside the event horizon but close to it can leave the event horizon can leave it but returns. While outside the event horizon can emitt another graviton, this one can return to the black hole or can leave it permanently.

Andrew Worsley

I hope you will take time to summarize your current understanding. You asked for feedback and ideas. Did you change your thinking, or clarify in any way?

Your question is not as efficient as it could be. Instead of "How can", try "Assuming that it can, how to detect and image?"

My own private view is that gravitational and electromagnetic effects depend on the same underlying potential field. And the potential field is itself identical to a physical vacuum with real, measurable properties. In other words, that "space time" is a physical field. I have tried hundreds of models with "superfluid, slightly compressible" tending to be slightly more useful. Again, my own private view, is that the gravitons are themselves fermions, with a mass distribution where the average speed is the speed of light and gravity. But the smaller particles have greater speeds. For a given environment, the fastest speed come with the smallest masses. But, overall, effective signal speed depends on detector sensitivity, layout and management.

For gravitational and electromagnetic effects any component where the free space wavelength is larger than, but comparable to the size of the object (black hole) can be useful as a signal for detector arrays. So I have tried to set up global magnetic and electromagnetic and gravitational detector arrays for nanoHertz to GigaHertz signals.

We all need better ways to share models. Words are rather poor conductors of physical and social phenomena.

Best wishes.

Nothing ever gets in in finite outer time.

As Einstein succinctly pointed out in his paper published on the same day as two disasters (Hitler invading Poland and the publication of some drivel by Oppenheimer & Snyder), black holes cannot possibly form in a universe of finite age since solutions involving infinite time dilation are necessarily unphysical. The premise of this question, that objects with event horizons actually exist, is therefore incorrect. And, as Otto just pointed out, even if they did exist, they would be incapable of capturing matter.

We know that the equations of special relativity do not, in and of themselves, prohibit superluminal motion - nor indeed travel backwards in time. Likewise, the equations of general relativity are purely mathematical, symmetrical in time and must be handled with care - especially by "mathematical physicists" who aren't fit to lick Einstein's boots.

Gravitational attraction exists between energies. Light is electromagnetic energy and black hole mass and spin is also energy. So gravitational attraction exists between them. But the gravitational attraction itself (also called the gravitational force) is not the energy. So black hole mass cannot stop it from escaping the event horizon. In Newtonian gravity and in general relativity, gravitational attraction is ascribed to negative gravitational potential energy. This potential energy is mathematically deduced by integrating the observed acceleration. But there is no experimental evidence for the negative potential energy. Based on this flawed concept is developed another flawed concept called zero energy universe according which the sum total of all the energies of the universe is always zero at any given time.

In the following quantum gravity theory it is proposed that the gravitational attraction and entanglement are due to indivisibility of the infinite motionless fundamental substance of the universe from which the entire universe is created. So the gravitational attraction is some kind of a stress within this substance and since it is not the energy, it cannot be confined within the black hole event horizon.

Similarly following articles also show that the electrostatic potential energy of Schrodinger and Dirac wave equation can be eliminated by utilizing a unitless ratio of accelerations in the wave formalism.

Chapter: Periodic quantum gravity and cosmology

In the book, The wave equation: An overview

Lionel S. Price (Editor)

Nova Science Publishers, N.Y. (Jan.2020)

https://novapublishers.com/shop/the-wave-equation-an-overview/

https://www.researchgate.net/publication/338621845_Periodic_quantum_gravity_and_cosmology

Periodic relativity: the theory of gravity in flat space time

https://arxiv.org/abs/0707.4539v10

Chapter: Hydrogen spectra_using Einstein's field equations

In the book

"The wave equation: An overview"

Lionel S. Price (Editor)

Nova Science Publishers, N.Y. (Jan.2020)

https://novapublishers.com/shop/the-wave-equation-an-overview/

https://www.researchgate.net/publication/338621783_Hydrogen_Spectra_Using_Einstein%27s_Field_Equations

Concerning the idea that it has supposedly been proven that things can travel faster than c (relative to local space-time), that is completely incorrect. The experiments involved have all been shown to be flawed, and nothing has ever REALLY been observed to be traveling even AT the speed of light save for light itself, and NOTHING has been observed traveling faster than that (many efforts have been made to look for tachyons, but none have succeeded in ever actually observing a single one). Even the presumably faster than light speed expansion of the space between here and objects beyond the 'edge' of the Observable Universe does NOT involve faster-than-light travel relative to any local part of the Universe. Regions approximately 3.26 million light years apart move at most at about 70 to 73 km/sec relative to any object inside that region as a result of the Universal Expansion (they can move faster than that due to their own "peculiar" motions relative to each other, but that's another matter entirely). It is only when distances approach or exceed 14 thousand million light years that the CUMULATIVE expansion of 70 to 73 km/sec per 3.26 million light years adds up to more than the speed of light; and since such regions ARE so far apart, that cumulative expansion rate does not violate nor have anything to do with the local speed limit.

In any event, gravity does not have to ESCAPE the event horizon. It is what CREATES the event horizon, and as noted in my earlier answer, what the local "escape velocity" is has nothing to do with local conditions, but only with the amount of central mass, and the distance from that "singularity". So I'm afraid that this entire discussion is much ado about nothing.

To Vikram Zaveri,

The often asked question on how a black hole can exert gravitational attraction on matter outside, in spite of the fact that the interior is causally shielded by the event horizon from the exterior world, has often been asked. Roger Penrose, for instance, has in popular talks answered this question simply and clearly.-- It should not be difficult to find his explanations. (Briefly, the gravitational field does not escape, but corresponds to that of the body before the collapse.)

To Norbert Straumann:

Explanation Of Roger Penrose (Briefly, the gravitational field does not escape, but corresponds to that of the body before the collapse.) is reasonable. Do he consider gravitational field as having negative energy? How is the energy created according to his theory? Or Do he believe in zero energy universe?