There ae several ways known, within general relativity. A nice summary is here:

http://large.stanford.edu/courses/2011/ph240/nagasawa2/

with the details available in the references.

Thank you Aleksei,

I think then, what I am not understanding is: if the black hole does not communicate its gravitation through the event horizon, how does the outside world know about the black hole's mass?  Or rather, how does the outside know how attractive the black hole is?

A nonrotating (spherically symmetric) black hole does not radiate gravitational waves. This is a consequence of Birkhoff's theorem, which basically states that outside a spherically symmetric object, the gravitational field depends only on the object's total mass, not on its radius or the internal (spherically symmetric) distribution of mass density.

A rotating black hole can radiate energy; however, this energy can be viewed as coming not from the inside of the event horizon but from the ergosphere, which shrinks as the rotation rate slows and the black hole approaches the spherically symmetric, nonrotating state.

As to the outside world knowing a black hole's mass, remember that the outside world never actually sees the event horizon form, as it is in the infinite future of any outside observer. So insofar as the outside world is concerned, the black hole forever remains in the process of formation, "frozen" in a sense. But even putting that aside, insofar as the gravitational field is concerned, what the outside world sees is the field that was "locked in" during the process of formation.

Thanks everyone.  I think my next question is then.... How does the curvature know how tight to be outside the event horizon?   In some way there has to be communication from the mass inside to the spacetime curvature outside.  Should I deduce that information does cross from inside to outside, but that information does not involve energy?  And therefore, that information is not massive and is free to escape?  I feel there is some sort of inconsistency here somewhere, but I'm not sure what it is.

As more matter falls into the black hole and it becomes more massive, it must communicate that fact with the curvature outside. I guess that's how it works. 

Steve: Even if you ignore the point I raised earlier (notably that from the viewpoint of an outside observer, the horizon remains at future infinity, so nothing is ever seen crossing it) the information about the amount of mass falling into the black hole does not have to come from the inside; it was always available on the outside. So there is no need to communicate any "new" fact from the inside to the outside.

Thank you V T Toth,

I think I might be beginning to understand.  Do you mean, from the viewpoint of an outside observer,  The material accumulates at the horizon and never passes through?  

Steve: That is indeed correct. Outside observers never see the horizon form. There is what is called a "surface of last influence" for infalling objects (see also the "MTW" book Gravitation, by Misner, Thorne and Wheeler): When an object passes through this point, a distant observer can no longer influence that object, as anything the observer sends, including light, would only catch up with the object inside the horizon. But this is something the observer never sees, as the object and the signal both appear to freeze due to extreme redshift as they approach the horizon. And no matter how long the observer waits, if that object happens to be a powerful rocket, it may choose to turn around and re-emerge... in the object's own frame of reference, only a very short amount of time may have passed, but in the reference frame of the distant observer, it could have taken eons and then some. This is an example of the extreme relativistic effects in the vicinity of a black hole.

Information is distinct from energy. How classical energy can be extracted from a black hole is known; information, however, is related to entropy. Entropy is infinite for a black hole in classical gravity and is finite only when quantum effects are taken into account. How this is possible is known for a special class of black holes-but what is, stll, not known is how to describe the dynamics in this case. It's important to understand the distinction.

If you are asking strictly about GR, and you are expecting an answer in QM terms (you mentioned gravitons), then the answer is that there is not a consensus on how to use the two theories together, especially in the case of black holes.

If you are willing to consider answers outside the scope of GR, then consider that gravity modifies potential energy of ALL objects and fields, and that therefore its presence is locally undetectable.  Physics can only detect energy differences.  This is also an important part of the equivalence principle ... observers cannot determine that they are in fact in a gravitational field.  They would have to have communication with remote observers to detect the energy (potential) difference.

Therefore you get some rather odd possibilities.  There is no restriction on the velocity of propagation of gravity, because it is not possible to communicate anything with it faster than you can get light signals into an area from an unaffected area (keep in mind gravity even affects the light signals as they are propagating).  So the "speed" of gravity is at present only an assumption.  If it propagates very fast, it would have very long wavelengths and would be undetectable by all of the current gravitational wave detection devices.

Such a postulate (faster propagation speed) would also allow it to propagate from black holes, without regard to the time dilation.  Consider this also ... black holes can be moved about in space as easily as any other object of the same mass which is not a black hole.  They are by no means frozen in space.  Only the positions of objects relative to the black hole get frozen.  Think of it as "sticky."

This postulate rules out gravitons as traditionally envisioned, because being energy they violate the postulate.  In my opinion, gravitons should be ruled out anyway, as they do not viably explain time dilation and spatial distortions associated with gravity.

Gravity is most likely related to entanglement.  Objects near a black hole are obviously "position entangled" with the BH, i.e. they are stuck there.

Dear Steve, you asked the question I asked myself many years ago and, after the time elapsed from then, I think that you are right if you want (with your question) to indicate that "when the matter disappears below the corresponding event horizon (into a black hole), the object must disappear completely, its gravity including". People attempt to suggest various exceptions to avoid this necessary conclusion, but either our deduction is strictly logical (then the disappearance of gravity is necessary) or is not strictly logical (and must therefore be incorrect).

I mean, the question is crucial and if physicists answered it, they would most probably found that the black holes cannot exist. (I started to believe in this claim recently after it appeared that the theory of neutron stars suffers from a serious imperfection: in all models, the metrics describing the stellar interior is torn away from the metrics describing the surrounding empty space. Such a discontinuity is physically unacceptable. The models with continuous metrics are possible, but all such models [at the moment, only those for a static and spherically symmetric object are known, however] yield (1) the outer physical surface above the corresponding event horizon and (2) disappearance of the Oppenheimer-Volkoff mass limit, i.e. we can construct a model for a stable object of whatever high mass. Hence, there is no argument supporting the existence of black holes. [On the other hand side, I must admit that there is neither any complete proof excluding their existence.])

Another aspect of your question is following. If we consider the concept of virtual particles mediating the interaction (gravitons in this case) and gravity is proportional to the energy or impulse of these particles, then the reduction of this energy due to the gravitational red shift of gravitons (they loose the energy in the gravitational potential) causes a corresponding reduction of the intensity of gravity. But because the gravity is, thus, weaker, it cannot reduce itself so much. Since it does not reduce itself so much, it must be stronger. But because it is stronger, its reduction of itself is larger, etc., etc. We can repeat infinitely these arguments. In terms of mathematics, the individual steps of this repetition would be represented by terms of  an exponential developed to the power series. Because the electric intensity obtained as a solution of Maxwell equations used to contain the exponential [exp(k*r)], I mean that the effect of weakening of the electric interaction/electric field by itself is included in the Maxwell equations. And, this is likely the reason of why there are not "electric black holes".

Thank you L. Neslušan for your very interesting response.  I am always interested in ideas that may not be textbook.  Again, thank you.

@L. Neslušan

I come back.  I was partially satisfied with an explanation given earlier.  That explanation was that an outside observer sees all material never entering through the event horizon. But with that scenario, I would still say that if the light cant reach us, or is so red-shifted that it's energy reaching us is zero, then why would we accept an argument saying that light cant reach us but gravity can?  Yes, I think I have convinced myself again that there is a contradiction here somewhere.  

@S.Faulkner

I add another comment about one important consequence of the effect of interaction weakening you might be interested in. As I wrote, the effect leads to the occurrence of exponential in an expression for the intensity of electric field, E. One can then derive the elementary electric charge in form "+i*q*exp(-i*omega*R/c)" (positive charge) or "-i*q*exp(+i*omega*R/c)" (negative charge; it is appropriate to choose the opposite charge as complex conjugate), where "i" is the unit of imaginary number, "q" is the size of the elementary charge, "omega" is the angular frequency associated with the particle according to the de Broglie relation "hbar*omega = m*c^2", "R" is a distance where the interaction is assumed to take place, "c" is the speed of light,  "m" is the mass of the particle, and "hbar" is the Planck constant divided by 2*pi. It is appropriate to gauge "R" as "R=hbar/(M*c)" (Compton wavelength for mass "M"), whereby "M=sqrt(alpha)*M_p" ("alpha" is the fine structure constant and "M_p" is the Planck mass; M ~ 10^{-9} kg).

Sorry for this relatively long "technical" introduction. Now, I can explain I would like. The function for the positive charge can be developed to serioes "q+ = i + m/M +..." and negative charge to "q- = -i + m/M +..." (the higher terms are neglected; it is possible, since for, e.g., proton the ration 'm/M ~ 10^{-18}

Re Neslušan:   "People attempt to suggest various exceptions to avoid this necessary conclusion, but either our deduction is strictly logical (then the disappearance of gravity is necessary) or is not strictly logical (and must therefore be incorrect). ... I mean, the question is crucial and if physicists answered it, they would most probably found that the black holes cannot exist."

For some reason, physicists are slow to think that contradictions might imply the theory in which a problem is embedded might not be correct.  Gravitational physicists are slow to think that a contradiction might also rule out a particular solution to some equation such as the GR field equation, even though quantum physicists use this technique to eliminate solutions. 

That said, there is an issue here even if black holes do not exist and all theoretical problems were "fixed."  Because even for ordinary masses, the implied spatial and temporal distortions that affect LIGHT do not seem to affect GRAVITY.  However, there is a caveat.  We have not detected gravitational WAVES, and in fact these distortions do not affect STATIC electric fields either, so maybe there is no inconsistency???

I can also argue that no amount of spatial curvature can affect any static field in the following way.  I'm talking about static fields of any kind, gravitic or electric.

Consider an observer in orbit at radius R.  You may consider this to be a reasonably large radius, perhaps comparable to the orbit of Earth or Venus or even Mercury.  Let us say there is a rather low density dust cloud of about one solar mass about which you are orbiting.  You detect an electrostatic and a gravity field of a certain strength.  The electric field you can measure by means of the motion of space probes on which you control the charge.  The gravity field determines your orbit.

Let us suppose this dust cloud is not so dense that it greatly impedes a light ray.  You can shine a light ray through it and by means of bending and Shapiro delay, deduce the curvature, and calculate the proper radius Rp1.

Now suppose the dust cloud collapses to a neutron star or even a quark star, barely larger than a black hole, so that the curvature is very great.  Shapiro delay becomes large, and light bending might even result in photon orbits.  Rp2>>Rp1.

However, you notice absolutely no difference in either gravitational or electric fields.  The part of the Schwarzschild metric outside the surface of a body is unaffected by the configuration inside the body, as long as it is uniform and symmetric.

It would appear, then, that the "proper" distance to the gravitational source (or the electrical source) has no physical meaning whatever to an observer who does not venture into that space, and no effect on static fields.  It only affects observers, or waves, actually traveling through it.  If we do not travel through this region, we could get by entirely without it.  A simple Hamiltonian analysis taking into account time dilation will give the correct precession of our orbit, and the other properties, bending and Shapiro delay, require traveling through it.

The static gravitational field of a black hole would be due to virtual gravitons. Those have no problem escaping across the event horizon.

@K.Kassner

Qualitatively, virtual gravitons should be able to escape out of the event horizon. This effect is however an analogue of that leading to the "evaporation" of black holes and, hence, we can expect that it is many orders of magnitude weaker than a normal exchange of the interaction-mediating virtual particles. I think, it cannot account for the principal answer of the Steve Faulkner's question.

@Robert Shuler

In this discussion, there are mixed two principally different concepts:

(1) theory of interaction mediated by the intermediate bosons;

(2) general relativity (GR).

The first concept is consistent with the quantum physics, in which the equivalence principle is, simply, ignored. (The Schroedinger equation contains the potential energy, therefore the properties of "central" field depends not only on the distance of a test particle from the centre, but it also depends on further properties of the test particles, e.g. on its mass or electric charge in the case of electrostatic interaction.) Consequently, the Birkhoff theorem you described, in fact, is not expected to be valid. With respect to the character of the Steve Faulkner's question (and in contrast to our discussion in other thread), I considered here the first concept.

I don't see what Birkoff's theorem has to do with the discussion.  Lacking any viable theory of how gravity and especially curved spacetime might be produced by QFT, I was answering only in the context of GR and various experimental evidence.  I state this for clarity of record in this conversation.  I don't wish to argue with anyone, and will unfollow the question if this degenerates.  I am tired of the irrational discussions on RG.

The question seems to presume that gravitational effects are continuously dynamically imparted to and from discrete objects much as EM effects are imparted to particles.

Since the gravitational waves described by GR seem to be the oscillation of gravitational effects (dimensional spacetime distortions) presented to a subject by primarily rapidly rotating binary systems, they cannot be the mediator of gravitational effects, as they are not produced by all gravitating objects - their oscillations are not statically produced produced solely in proportion to the density of discrete masses.

As I understand, this also argues against any quantum mediation of gravitational effects.

As V. Toth commented on page 1, "... insofar as the gravitational field is concerned, what the outside world sees is the field that was "locked in" during the process of formation" - the gravitational effects described by GR ('curved spacetime') may result from the process of accretion.

As I understand, the collapse of massive objects such as stars are initiated not by any (even quantum) gravitational interaction among dust and gas particles - but by EM interactions among charged particles. If this process also produced the effects of curved spacetime, along with subsequent gravitational interactions, gravitation may be an emergent interaction of curved spacetime rather than any propagation of material energy among particles or objects.

In this view, gravitation only emerges as spacetime becomes curved by accretion - the localization of material mass-energy.  The accretion of massive objects necessarily involves an equal and opposite reaction - the depletion of mass-energy from the surrounding vacuum.  This suggests to me that the (relatively static) curvature of spacetime may result from the flow of mass-energy from the vacuum to condensed objects during the process of accretion...

James, to first order I agree with your comments above.  I see two wrinkles.  First, the quantum gravity theorists do propose relatively conventional gravitational mediation.  I have opened a question thread on this, by the way, which I'll link below.

Second, the spacetime structure around a massive object must interact with the rest of the universe much faster than time progresses inside that spacetime structure.  For example, such an object can be moved about and accelerated (if it is orbiting, it is continuously accelerated).  Consider a near black hole orbiting a neutron star for example.  Many short time events affect its trajectory.  Yet for objects deep in its field, time progresses very slowly.  Yet their position relative to other objects in the universe changes rapidly.

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

Robert,

I generally agree with your points - I stipulated that the spacetime curved by the accretion of an object of mass is relatively static as they may dynamically gain or lose mass (further accretion or supernovae, for example).  I also agree that the spacetimes of gravitationally interacting massive objects may also alter each other, at least peripherally.

BTW - any object exhibiting the characteristics of a stellar collapse black hole would not be orbiting a less massive neutron star - they would both orbit their collective center of mass, correct?

Yes correct, I always assume I can post informally here and people will  conclude the details, unless there is a specific question about the details.

@Neslusan:

"Qualitatively, virtual gravitons should be able to escape out of the event horizon. This effect is however an analogue of that leading to the "evaporation" of black holes and, hence, we can expect that it is many orders of magnitude weaker than a normal exchange of the interaction-mediating virtual particles.."

No, this is not the same thing. Hawking radiation has to do with pairs of virtual particles, one of which has to have negative energy. I was talking about single virtual gravitons. These are much more frequent. By the way, black holes also can have a charge that is visible outside. How does its electric field get beyond the event horizon? Because the charge emits virtual photons in enormous quantities.

The lower the energy of a virtual graviton or photon, the more frequently it will appear. In the case of charge, we are not talking about photons in the visible range of the spectrum, but of photons in the hertz and milli-hertz range and below. The number density of virtual gravitons or photons in a static gravitational or electric field diverges as the frequency goes to zero (the energy density remains finite). This accounts quantitatively for the existing field. Which is largely unaffected by the event horizon, because it is dominated by virtual particles at such low energies that their number density is not much diminished by the horizon.

" I think, it cannot account for the principal answer of the Steve Faulkner's question."

Of course, it can. It is the canonical answer in field theory. It is not just a hypothesis made up by myself.

I also brought up the static electric field in a prior post.  No one took the bait. 

The interesting thing is that from a given radius just beyond the surface of a collapsing object, as it collapses, the proper "radius" increases and tends toward infinity as the object approaches full gravitational collapse.  But this very real physical distance does not affect the field at all.  So is it really a very real physical distance in all respects?  Well, not in respect to the static field.

K. Kassner,

Can the same virtual graviton-mediated exchange of material gravitational energy also explain the mass-proportional gravitational effects produced by the Moon, for example?

Also, aren't EM field effects observed outside of black hole event horizons those produced by accreting external matter - rather than those produced by any EM charge of the black hole itself?

Robert,

Isn't the increase in proper distances accounted for by length contraction, so that us external observers would not see the increases?

 James,

"Can the same virtual graviton-mediated exchange of material gravitational energy also explain the mass-proportional gravitational effects produced by the Moon, for example?"

Yes. The field-theoretic explanation of all static fields is in terms of continual exchange of low-energy field-generating particles. It is a dynamic explanation of a static phenomenon.

"Also, aren't EM field effects observed outside of black hole event horizons those produced by accreting external matter - rather than those produced by any EM charge of the black hole itself?"

I guess so, if any EM effects are observed. I don't think anyone has ever presented experimental evidence for a charged black hole. But charged black holes do exist in theory (Reissner-Nordström solution), so the question how theory could explain an observable charge of a black hole is legitimate. People believe that real black holes will have lots of occasions to get rid of their net charge before collapsing. Electrical charges come with two signs and tend to eliminate each other before any appreciable static charge can build up.

James, my primitive understanding is that length contraction is one "interpretation," and I would offer that the lack of change of static fields suggests that interpretation is physical.  However, expanded space without length change is another interpretation that results in so-called "funnel" diagrams.  This second interpretation becomes necessary for things like wormholes that tunnel outside a region of space, for example.

Robert,

Thanks - I guess that begs the question of how physical funnel diagrams and wormholes are for non-local observers...

K. Kassner,

"The field-theoretic explanation of all static fields is in terms of continual exchange of low-energy field-generating particles. It is a dynamic explanation of a static phenomenon."

Thanks. It's difficult for me to envision how the tidal effects of the Moon on the Earth's oceans, for example, could be the net result of low-energy exchange of (virtual) particles from the Moon and from the Earth...

"... But charged black holes do exist in theory (Reissner-Nordström solution), so the question how theory could explain an observable charge of a black hole is legitimate."

Wouldn't that question be made legitimate only by the observation of otherwise unexplained external EM fields?

I don't recall the references offhand, but papers have been written trying to deal with the disappearance of charge and mass and other conserved quantities into a black hole, worm hole, etc.  I think this is related to the horizon time dilation problem, for which there are several discussion threads, including one of mine. 

Bottom line is, due to time dilation, the charge, mass or other conserved quantity never actually crosses the horizon and becomes unobservable.  Only in the proper time of the falling object can the event horizon be crossed, and by then the outside universe has passed away into history and no longer exists.

James,

"Wouldn't that question be made legitimate only by the observation of otherwise unexplained external EM fields?"

No. I think, consistency questions within a theory are always legitimate. We have the Reissner-Nordström solution describing a charged black hole. I.e., the electric field lines come from the interior of the horizon, crossing it. Therefore, we may wonder whether this is in conflict with what we know about transport of electric fields in space. The answer is that while electromagnetic waves cannot pass the horizon (the wrong way!), a static electric field can, and this is, in the dynamic picture of static fields, due to the fact that virtual particles are less restricted in their motion than real ones. There is also an interpretation of tunneling of particles, in which the tunneling process itself is not restricted by the speed of light (even though information will not travel faster than light).

Robert,

"Bottom line is, due to time dilation, the charge, mass or other conserved quantity never actually crosses the horizon and becomes unobservable. Only in the proper time of the falling object can the event horizon be crossed, and by then the outside universe has passed away into history and no longer exists."

This would be an inconsistent answer. The universe does not pass away, while matter  "tries to cross the horizon". The idea of simultaneity behind this picture is Newtonian and wrong. Matter near the horizon can never see anything beyond a certain finite external time from the outside. So the "whole history of the universe" does not pass before their eyes for those observers hanging around the horizon. The situation is, apart from the fact that the external time need not be chosen as Schwarzschild time, quite asymmetric. Even in the case that we describe external events using Schwarzschild time, there is an absolute upper and finite limit, beyond which information cannot catch  up with the infalling observer, so the outside exists well beyond the time of his infalling (even beyond the time he reaches the singularity).

The point is of course that there is no such thing as a universal time ("chosen by physics" instead of "chosen by humans") in all of the cosmos. So there is no unique way of associating a time at which the matter crosses the horizon with a time of an external observer. There are different ways of doing this, some of which lead to the time of the external observer becoming infinite, others to it remaining finite. What can be said, however, is that spatiotemporal intervals between events corresponding to particles crossing the horizon and external events (at large but finite distance) remain finite. So there is a precise sense, in which the matter does cross the horizon.

Moreover, the Reissner-Nordström solution, in which a black hole does have a charge, has the charge inside the horizon. And finally, also the mass of a black hole is inside its horizon, not outside, according to the Schwarzschild solution.

K. Kassner,

"... consistency questions within a theory are always legitimate. "

I agree that such questions may be valid within a specific theoretical context, but may not be generally valid outside that context - thanks.

Conceptually, at least, aren't space and time aspects of a single system of coordinates, so that any effect that can be attributed to time dilation could also be attributed to length contraction - especially as it relates to infinities?

K. Kassner - interesting term, spatiotemporal intervals

Klaus, I did not give "my" opinion.  I have none.  I was giving the opinion of many luminary authors from Hawking to Susskind, that an observer crossing an event horizon sees the future history of the universe on the way down.   I think you should not confuse us simple RG posters with your new theory to the contrary.  : )

Robert,

I am sure that neither Hawking nor Susskind ever said such a nonsense (about an observer seeing the future history of the universe on his way down) :-). They understand general relativity too well. Nor am I posting my new theory. All that I am discussing is ordinary mainstream general relativity [1]. It may sound new to people not knowing the theory well, but experts will certainly agree with me.

[1] Kanai, Yuki, Masaru Siino, and Akio Hosoya. "Gravitational collapse in Painlevé-Gullstrand coordinates." Progress of Theoretical Physics 125, 1053-1065 (2011).

Oh yes, definitely.  That is the mainstream view.  Susskind, The Black Hole War, page 74: "If you, suspended near the horizon, and I, in the space station, had telescopes, we could watch each other.  I would see you and your clock in slow motion, while you would see me speeded up like an old Keystone Kops movie."

I'm sure you will say now you meant something different, but this is what I meant all along.  Simply take it to the limit upon approaching the horizon and the speed up factor becomes infinite.  I've seen more detailed discussions, but this one was easy to put my finger on right now.

I do not like to accuse my friends on here of speaking nonsense, even if they are.  But since you have leveled the accusation at me, I will level it back.  I'm a bit tired of the holier than thou posters.

James, your comment about symmetry of length contractions and time dilation was interesting, but two caveats...

• It really only holds for isotropic coordinates.  Schwarzschild coordinates are only approximately isotropic.  In strong fields there is a difference.  I don't know what the origin of this asymmetry is.
• To get the coordinate velocity of light to come out right, we must assume length contraction (or its alternate interpretation of spatial expansion) along with time dilation.  But energy differences are completely accounted by the time dilation (e.g. photon frequencies).  So there is a startling asymmetry there of what you can say about one vs. the other.

Robert,

"Oh yes, definitely. That is the mainstream view. Susskind, The Black Hole War, page 74: "If you, suspended near the horizon, and I, in the space station, had telescopes, we could watch each other. I would see you and your clock in slow motion, while you would see me speeded up like an old Keystone Kops movie."

This is not what we were discussing. Of course, there is time dilation and the local observer at the horizon will see the distant observer speeded up. If he managed to stay at the horizon forever, he might even see the history of the whole universe (but it would never finish in a finite time of his).

We were talking about an infalling observer in free fall. In the finite proper time that it takes for him to reach the horizon, he will not see an infinite amount of time passing at the outside, and as I said, Susskind never pretended this kind of nonsense, because what you are citing now is not what you claimed before. The universe does not pass away in the time it takes the infalling observer to get to the horizon. On the contrary, one can calculate a finite time (proper time of the distant observer), beyond which no light from the distant observer can reach the infalling observer anymore, before he falls through the horizon. So he cannot see the history of the distant observer beyond that time. It is in the textbooks. (MTW, for example.) This is the old problem that the integral of something that gets infinite may remain finite...

You know, precision of quotations is of some importance in science...

I told you that you would say that was not what you were talking about.  But it is not true.  I had to look back two days to find the original comment.  It was in the context of  "Bottom line is, due to time dilation, the charge, mass or other conserved quantity never actually crosses the horizon and becomes unobservable.  Only in the proper time of the falling object can the event horizon be crossed, and by then the outside universe has passed away into history and no longer exists."

I did not make this up, by the way.  I read it in some paper, and I'm looking for it but have not found it yet.  I wouldn't propose it (or anything regarding an event horizon) as proven fact.  But it makes reasonable sense, and it was appropriate to offer it in response to Steve's question.

Time is a bit ambiguous when observers are not at the same point, but certainly by the time the charge or mass crosses the horizon it is beyond the ability to influence anything at a higher observer's position prior to basically "the end of the universe" or some such far time as no one cares.  If we look at it from the higher observer's viewpoint, for that same near-infinite period of time, there is something visible near the horizon which could emit photons or gravitons, however red shifted they might be, which would reach and affect the higher observer.

So my comment stands, I am right about what I said, I thought it was interesting to add, if you disagree it is not necessary to be caustic or even to say anything.  If the other posters were interested in reading a harangue, they'd have chimed in by now.

Robert,

"Only in the proper time of the falling object can the event horizon be crossed, and by then the outside universe has passed away into history and no longer exists."

This is factually wrong, and that was the only reason I commented on it. I am not making up own theories (here). My purpose is to explain general relativity (and to some extent defend it, because it is much better as a theory than most of the alternative bits and pieces of "explanation" offered here), not to make up things. If this is perceived by some as "new" theories, it is only, because they do not know the "old" theory.

Now why is your statement factually wrong? It is wrong on two counts. First you say that "only in the proper time of the falling object can the event horizon be crossed". This is wrong, because there are several global time coordinates which remain finite on horizon crossing. These are the time of the Gullstrand-Painlevé metric (my favorite, evidently), the time of the Kruskal-Szekeres metric and the time of the Eddington-Finkelstein metric, and there are more, some of them without name yet. These all describe the Schwarzschild geometry. Because they remain finite, it is wrong, within general relativity, to insist "only in the proper time...".

Second, your statement about the outside universe having passed away, which you might find in some popular descriptions (but not by people like Hawking who know their stuff well), is also wrong. It is not a statement of a fact. In all the alternative metrics I have mentioned, the time of an external observer at which the horizon is crossed (according to that observer) remains finite. How can the universe have passed away, if only a finite time has ticked off on the external observer's clock? There is one time coordinate, the Schwarzschild one, that becomes infinite at the horizon, because the Schwarzschild metric becomes singular there. Spacetime does not become singular as has been proven by Kruskal and Szekeres. If you describe things in this singular coordinate, the crossing of the event horizon becomes simultaneous with exterior events that have infinite time coordinate. But that is the consequence of an unlucky definition of simultaneity, nothing more. Simultaneity at a distance is not a physical category. All that is physical between pairs of distant events is whether they are timelike, null or spacelike. And what can be said about the horizon crossing in terms of spatiotemporal relationships is that the interval on world lines of exterior observers that is spacelike with respect to the infalling observer gets infinitely large on crossing the horizon. (A fancy way of stating a triviality.) But most of this interval remains unknowable to the infalling observer.

"So my comment stands, I am right about what I said."

No, you are wrong, and in science this is not a question of opinions.

@ Original question.

It seems that the discussion proceeded from the question of how can gravity escape from the black hole to that of how can something be observed (by an outer observer) to the opposite effect of the fall into this object. In this context, I would like to point out (to discuss?) on a concerning effect: dependence of the GR speed limit on the gravitational potential/curvature of spacetime. Namely, a photon should move along the zero geodesic and, hence, it speed is lower in a curved spacetime in comparison to the value in an empty space (without any matter). This real the effect of the behaviour of a photon (not how it is seen by outer observer).

In the limit of an approach the event horizon, the speed limit is reduced to zero. So, there appears a "black-hole-enter" Zenon paradox. How can something, in its real time, reach the event horizon when its speed is, necessarily, slowed down to zero in the approach.

Neither this is any new theory. I am only attempting to apply the same principle, which is used to explain, e.g., the bending of light rays closely above the solar surface, to the falling of things into the black hole.

@K. you are only nit picking informal language.  I doubt (and would be very interested if there is) a meaningful observer-based real coordinate system in which one can cross the event horizon other than proper coordinates.  Of course there could be various derivatives and relatives of the proper coordinates.  We are making posts, not writing a textbook, and nothing in my post was outside GR.  I was just reporting an interesting possibility I read about in several places.  I have also read papers emphasizing that in-fallers disappear in the frame of distant observers, indicating some disagreement among people about what GR says.  It's not something that keeps me up at night.  You are way overdoing it.  As far as the outside universe, a figure of speech.  It will be so far in the future that the configuration of the universe will be very different and we won't be there.  So in effect the current universe passes away.

Robert,

"You are way overdoing it.  As far as the outside universe, a figure of speech.  It will be so far in the future that the configuration of the universe will be very different and we won't be there.  So in effect the current universe passes away."

What makes you think that? The universe will pass away in two months' time? An observer falling into a black hole the size (= mass) of the sun from a distance of  one astronomical unit will hit the horizon after two months, if Gullstrand-Painlevé simultaneity is used. Which means that he cannot see more than roughly (*) two months of the history of the universe (from the time of his departure) up to a distance of 1 astronomical unit and less to farther distances. (This statement is true independent of any coordinates. But using Gullstrand-Painlevé coordinates, it is possible to see it without calculation, contrary to Schwarzschild coordinates, where surfaces of simultaneity are much less favorably tilted.)

(*) I have not counted in the time he takes from the horizon to the singularity, where he could still see things, in principle. But that time is in the subsecond range.

Well, maybe it doesn't answer Steve's question, but it certainly seems valid for me to have reported it.  I'm skeptical of a coordinate dependent notion of who can influence what, because we have to maintain the same physical outcomes in all coordinates.

Robert,

The "time" at which a distant event happens, is not a physical outcome. Most times in GR are just coordinates. And that simultaneity is a relative notion, should be well-known to anybody having looked into the subject of relativity :-).

Nobody said anything about the time at which a distant event happens.  We were discussing whether an event at A can "influence" an event at B.  This is coordinate independent.  There must be only one outcome.

Sure. Nobody disputed that. A can influence B, if they are timelike and A is in the past of B. This is coordinate independent. But I do not see the relationship with the preceding discussion...

L. Neslušan,

"In the limit of an approach the event horizon, the speed limit is reduced to zero. So, there appears a "black-hole-enter" Zenon paradox. How can something, in its real time, reach the event horizon when its speed is, necessarily, slowed down to zero in the approach. "

As I understand, the proper speed of an infalling particle (photon) is maintained – it only appears to stop for external observers. The proper speed (of photons, for example) continues (at the speed of light), but for external observers it is traversing 300k highly contracted meters each highly dilated second.

@James Dwyer

About a half year ago, I would certainly accept of your (and commonly accepted) representation that the light speed is reduced only for external observers. However, there appeared one serious argument that now lead me to doubt. Please, allow me to outline an explanation.

An attempt to describe the metrics of the spacetime inside and around a (spherically symmetric) neutron star revealed that this metrics is, principally, discontinuous at the stellar surface. The internal structure of neutron star is described by the field equations and equation of state, whereby all equations contain some constants, which are composed of the fundamental constants including the speed of light, "c". I found that the discontinuity is the consequence of the fact that the value of "c" valid for a free space (without matter) is considered in the equations. Supplying of this value is consistent with the representation you described.

The continuity can be achieved, if the free-space value of "c" is replaced by the "reduced" value (valid for a given, specific star-centric distance). However, this implies the reduction of "proper speed", I think.  The state of stellar gas cannot probably be dependent of what an outer observer sees. Or, it would be strange to argue that the metrics becomes (after the correction of "c") continuous for outer observer, but actually remains torn one away from other.

L. Neslušan,

"In the limit of an approach the event horizon, the speed limit is reduced to zero. So, there appears a "black-hole-enter" Zenon paradox. How can something, in its real time, reach the event horizon when its speed is, necessarily, slowed down to zero in the approach."

If I understand, I certainly agree that particles cannot freely propagate through neutron star material, but the prior statement seemed to be applied to the external event horizon of a black hole – where only relativistic effects are influential. My statements should apply only to those conditions of an independent event horizon - which do not slow particles' ‘real time’ speed 'down to zero'.

In my own view, high speed particle collisions cause the disintegration of infalling compound particles, releasing their binding mass-energy and allowing reduced mass elementary particle residue to be ejected on their approach to an event horizon – probably within the black hole corona...

@James Dwyer

One more note to the slowing the speed of light down at the neutron-star surface: The continuity of the metrics at the surface requires not only a reduced value of the speed inside the star (in distances r < R_{out}), but also (immediately) above the surface (in distances r > R_{out}), in the vacuum.

I should precise my claim about the Zeno paradox. I mentioned only the fact that (if my considerations are correct) the "proper" speed of light is slowed down to exactly zero value only in the distance of event horizon. Before this horizon is reached, the speed is finite (though decreasing). I have not calculated a "efficiency" of the paradox and answer the question if the horizon can be or cannot be reached by a particle in a finite time. In the case of reduced light speed, the slowing the velocity down would only exclude the free fall, if the second possibility appeared to be relevant.

The Penrose process (also called Penrose mechanism) is a process theorised by Roger Penrose wherein energy can be extracted from a rotating black hole.That extraction is made possible because the rotational energy of the black hole is located not inside the event horizon of the black hole, but on the outside of it in a region of the Kerrspacetime called the ergosphere, a region in which a particle is necessarily propelled in locomotive concurrence with the rotating spacetime. All objects in the ergosphere become dragged by a rotating spacetime. In the process, a lump of matter enters into the ergosphere of the black hole, and once it enters the ergosphere, it is split into two. The momentum of the two pieces of matter can be arranged so that one piece escapes to infinity, whilst the other falls past the outer event horizon into the hole. The escaping piece of matter can possibly have greater mass-energy than the original infalling piece of matter, whereas the infalling piece has negative mass-energy. In summary, the process results in a decrease in the angular momentum of the black hole, and that reduction corresponds to a transference of energy whereby the momentum lost is converted to energy extracted.

The maximum amount of energy gain possible for a single particle via this process is 20.7%.The process obeys the laws of black hole mechanics. A consequence of these laws is that if the process is performed repeatedly, the black hole can eventually lose all of its angular momentum, becoming non-rotating, i.e. a Schwarzschild black hole. In this case the theoretical maximum energy that can be extracted from a black hole is 29% its original mass. Larger efficiencies are possible for charged rotating black holes

This link below shows the effect of experimental verification that gravity fields have mass (which is missing from the GTR) limits black holes allowing redialy traveling gravitions and photons to escape with reduced mass. But photons with transverse components end up in a finite orbit if mass of the hole is big enough.

https://drive.google.com/open?id=1J4_5nGoZMiFo4Tdq3_tpzgPEO4DwYRmO