In Black hole theory, have mathematicians finally lost all connection with physics?

Dear James,

an *asymptotic* observer seeing a freely-infalling object towards the horizon would see the following: the object would *decelerate* whilst approaching the horizon, and freeze in motion. That's why a black hole in Russian is called a "frozen star". But, as you correctly explain, its visibility would decrease due to decrease in radiation wavelength as well as luminosity.

However, you are mistaken in the following if I have understood your little paper correctly: material particles may very well cross the horizon *in their own reference frame*. Because the horizon itself need not be a place in spacetime with high curvature. Therefore no high acceleration needs to be there. The more massive the black hole, the less curvature and acceleration *near the horizon*.

This is all classical general relativity, of course. It all changes, however, when semiclassical effects are taken into consideration.

Best regards

Oliver

Oliver, you've reiterated what I've been criticizing. You along with others are conflating the slowing of clock-speed with increasing acceleration. It is fundamental to relativity that speed in space and speed in time are inversely related. Imagine observing the fall of an object into a black hole from the moment you drop it from a safe distance: It begins accelerating, as it would toward any gravitational vortex. It continues accelerating as its clock decelerates. It is continuous.

"the horizon itself need not be a place in spacetime with high curvature"

The horizon is a place so extreme that light cannot escape. It has just as severe a curvature for those going in as for those going out. This is implicitly recognized by the conventional theory, that clock-speed approaches zero on the way down; in relativity, when clock-speed approaches zero, speed in space approaches c. Those differences aren't relative to an observer -- it is well-recognized that clocks really do go slower the deeper they are in a gravitational field.

Just to expand on my previous answer to Oliver: It is a belief apparently universally shared by everyone working on black hole theory. But there is nothing in relativity theory to suggest that an object will appear to an observer to be accelerating slower the more it accelerates. And there is nothing in relativity theory to suggest that observed motion in space and observed motion in time are anything but inversely related. It is an unsubstantiated belief, due apparently to a simple confusion of time-speed with space-speed.

Dear James, I don't know what you mean by space-speed and time-speed. What I re-iterate though is standard textbook knowledge, nothing else. The scenario of an infalling particle observed by an asymptotic observer is completely understood, mathematically and physically, in standard relativity.

Also, please bear in mind that the "acceleration" you are speaking about is a local notion, and you are implicitly referring to the inertial system of the infalling particle. An asymptotic observer has no means to measure the local acceleration of the infalling particle. However, (s)he *sees* a decelerated particle while looking upon it. Note the difference between "seeing" and "observing" which many textbooks emphasize. The situation is different in special relativity without acceleration where the inertial systems are fit to map the whole of (Lorentzian) spacetime.

Also, as I said, the horizon itself is not a special place from a curvature point of view, but from a causal point of view. As I correctly stated, tidal forces near the horizon of a BH depend on the mass parameter of the black hole: the more massive they are, the less the tidal forces.

This is all standard textbook knowledge. If you say it's wrong, you say that general relativity is wrong.

Oliver

Oliver, I am saying the "standard textbook knowledge" is wrong precisely because it does not conform to relativity.

Bodies will be observed to accelerate as they fall toward massive objects, whether they are planets or black holes. Their clocks will be observed to slow from the perspective of a distant observer in direct relation to their observed spatial acceleration. In other words, acceleration in space corresponds to deceleration in time.

Drop a clock from a stable elevation above a black hole. Its fall toward the event horizon will accelerate just as it would if dropped from an elevation above the earth. It will accelerate until it reaches the event horizon just as it would accelerate until it reaches the surface of the earth. There is no fundamental difference. And the faster a clock accelerates as it falls, whether it is toward a black hole or the earth, the slower the clock will be observed to tick.

To think otherwise is simply mistaken. No matter how many textbooks say otherwise, what they are claiming is that a clock will be observed to fall faster and faster until at some point it will be observed to fall slower and slower. That isn't relativity; when considered carefully, it is absurdity.

Just as with relative uniform motion, faster in space is slower in time. A clock that is moving close to the speed of light will be observed to be ticking in "slow motion."

Daniel Pfenniger

The mistake of James is to not grasp that GR equations are local, which translates to differential equations constraining locally space-time. The local constraints are the ones of special relativity including the local speed of light constancy, the differentiabiliy (smoothness) of space-time, and the principle of equivalence assuming that the local laws of physics are the same locally in any free-falling frame.

So tiny objects crossing the black-hole horizon are not subject to any other local rules than other free-falling objects. Tidal stress is a second order effect that vanishes in the limit of the object zero size.

When one solves the GR differential equations given boundary conditions, one finds the relationships between distant observers. All over the solved domain GR local constraints apply. It is then illogical to assume that the local rules of GR apply, and with given reasonable boundary conditions (flat asymptotic space-time, spherical geometry) that the non-local solutions are wrong.

It is not the connection with physics that is of concern but the connection with Nature. If there be black holes - and astrophysicists claim there are (including a 4 million solar mass behemoth at the center of our Milky Way galaxy) - the events just outside the event horizon must be a complete jumble of processes produced by the infalling material such as to defy conventional description. Certainly physics applies in this region but with the higher order terms included. You might speak of the slowing of infalling clocks but you never would be able to read the clocks from afar to read the time. To an observer travelling with a clock, the clock wouldn't slow it would be pulled asunder! We know not the physics within the black hole and are barely able to comprehend the physics immediately external to the black hole. But not to worry, Nature surely has everything under control and how presumptuous it is of us to demand the detailles..

Daniel, are the great lights of black hole physics subject to your same critique? They have made the claims I've only criticized. So I wonder.

True, an observer's clock can only tick in proportion to her own heartbeat. Who could disagree?

But when you write of things unobservable that defy presumption, it is much like saying we cannot know the physics of sound in an especially dense forest if we are not in the forest when a tree falls. So I disagree.

If you are one of those who hasn't accepted the tenets of Relativity we have nothing to discuss here. If not, then I protest: We know that if a body falls in a gravitational field, according to Relativity, it will appear to accelerate in space and decelerate in time. But without contesting that simple and well-established tenet, conventional Black Hole Theory holds that a body's clock AND speed will appear to decelerate as it approaches an event horizon. Does a body at first accelerate toward a black hole like it would toward any massive object, and then at some definite point begin to decelerate for some reason? I've never seen the question addressed, of how such a remarkable transition might occur. Have you? Is it presumptuous of me to ask?

Dwight and Daniel, I apologize for attempting to respond to Dwight by addressing my response to Daniel.

Daniel, my overall response to you is, primarily, the same as to Dwight. The authorities have made the claims I've only criticized.

General Relativity isn't constrained by locality. The Principle of Equivalence (which was invoked for Special Relativity) aside, GR addresses the universe on the largest scales. It applies to the behavior of bodies in gravitational fields: large-scale curvatures like the bending of light near the sun. And nowhere in Relativity (SR or GR) is it contended that variations in observed time-speed and space-speed are anything but inversely related.

Dear James

Forgive me for butting in but I think none of us should accept the "tenets of Relativity". In science, one must always keep an open mind, question always and be on the look out for new ideas and paradigms. I, for one, find Relativity to be very beautiful and powerful but I'm up for a new, improved version should one happen along.

Daniel Pfenniger

Dear James:

Sentences in your last post shows that you haven't grasped seriously GR (e.g. "General Relativity isn't constrained by locality."). So before pretending correcting the experts in GR, my advice is more humility: read, study and understand first the arguments at play, instead of displaying ignorance in public.

Well, that's harsh, isn't it. In another era, you could just as well counsel someone to study the experts on epicycles before publicly and presumptuously opening his mouth.

My advice to you is to consider the issues when discussing physics, not the sanctity of the holy fathers.

"GR local constraints apply. It is then illogical to assume that the local rules of GR apply"

A falling body doesn't appear to accelerate then decelerate when gravitating. Not locally, not vastly. Take off your conical hat when arguing physics.

Dear James: I can fully understand Daniel's frustration as it so often happens that experts in their field have to defend their statements to people who are obviously not, but have no problems claiming that all others are wrong, as are textbooks etc.

I have explained to you twice in this discussion that your statements are wrong, and Daniel has correctly pointed out a vital misunderstanding of yours, yet you never try to understand what we are saying.

So what is this discussion about anyway?

Somebody said something about "deceleration" upon appoaching the event horizon of a black hole. Of course, infalling material is accelerating under gravity as it approches the event horizon and is traveling along a geodesic of increasing curvature. To a distant observer it will appear that the material is slowing down because the clocks in the material's reference frame are running increasingly more slowly relative to the clock of the distant observer. The material however is still "falling" pell-mell into the black hole along its curved geodesic which it perceives as acceleration along a straight line.

Schematically, let us suppose that the material starts its descent into the black hole along the z axis of the observer's (x, y, z, ict) reference frame and let (x', y', z', ict') be the reference frame traveling with the infalling material. As the descent proceeds and the material's velocity becomes relativistic [relative to (x, y, z, ict)] , the material's reference frame rotates around the z axis of the observer's reference frame. What the observer sees is the motion of the material in its (x', y', z', ict') reference frame projected onto his (x, y, z, ict) reference frame. In the (x, y, z, ict) reference frame the (x', y', z', ict') reference frame will be seen to be slowing down. This is the consequence of the curved geodesic tarjectory of the infalling material.

Oliver and Dwight, you are experiencing great frustration. Try to imagine mine.

I've tried to point out that the clock of a body moving uniformly or with acceleration will be observed to go slower the faster its velocity or acceleration. There is an inverse relationship. The clock and the spatial acceleration of an observed body don't both appear to go more slowly as it falls toward a black hole. Clock: slower. Spatial acceleration: faster. That is basic textbook Relativity -- except, startlingly, for specialists on black holes. It even clashes with common sense: Drop a cannonball from a tower and its fall will accelerate; let the earth morph into a black hole as the ball is falling and it will accelerate ever faster as it nears the surface-turned-horizon.

Dear Dwight,

Methinks you are now contradicting yourself and your previous comments.

A distant observer will not *see* an acceleration of an infalling object, and I am wondering how you would define "acceleration" and "velocity" in the first place, as both are locally measured quantities. All he sees is a spherical formation of a black hole, both visually decelerating and optically fading in this process.

I am beginning to think that you, too might be confused about local measurement of velocity: an interesting textbook exercise e.g. is to calculate the velocity of the infalling particle measured by a "radial" observer at a fixed value of "r" as the particle passes by (hence *local*!). It turns out that as the fixed value of "r" as a parameter tends to the Schwarzschild radius R_S, the velocity of the infalling particle tends to the light velocity "c".

However: this scenario is neither a velocity measurement by an infalling observer (because he would measure zero acceleration by definition), nor is it a velocity measurement by an asymptotic observer (because he would not be local).

Best regards

Oliver

Dear All,

How do we watch a hypothetical object descend into a black hole? Well, we place ourselves in orbit around the black hole at a safe distance and make the assumption that we and the black hole are stationary with resepect to each other and all infalling objects. Now we look out and see an object passing by us on a trajectory that will carry it directly into the black hole. We wish to watch it as it falls to its doom. How do we see it - we need light! Lets quickly run over and install a powerful sodium arc lamp on the object and direct it to shine "upwards" in our direction. Now we have not only a brightly illuminated object to follow but also the two sodium D lines whose Doppler shifts we can monitor.

What happens? The object falls accelerating and its rate of descent becomes relativistic. Presumably its clocks will begin to run slow as viewed from our vantage point. All the while we have been using the classical Doppler effect to keep track of the object's descent velocity which now becomes the relativistic Doppler effect that takes relativistic time dilation into account. At this point another effect also comes into play. The light from the sodium arc lamp we attached to the object now must ascend "upward" against the gravitational pull of the black hole below. So the falling object nominally would seem to be subject to two relativistic effects: From special relativity we have high-velocity (relative to our reference frame) induced time dilation and from general relativity we have gravitationally induced time dilation. Are these separable effects? How do they combine? The redshift eventually, all else being equal, will cause the object to fade from view. Would not the Doppler redshift imply increasing velocity of the object and thus continued downward accelation? Collision with other in-streaming materlia might slow and heat the object (possibly to astronomically high temperatures). The question becomes moot, of course, once the object, its clocks and its arc lamp are rent asunder by gravitational tidal forces. Maybe Wikipedia has the answers. I haven't looked.

From a practical point of view, it would seem that relativity only allows a limited view of the fate of material falling into a black hole.

Dwight,

I've read your pdf on time dilation and length contraction, and I agree with your assessment that relative high velocity and time dilation are co-related, and inversely so.

I've expressed the relativistic relationship in a simple diagram that avoids Minkowski's mistake of projecting the observer's clock on the world-line of the observed (as when light is represented as moving in time). It illustrates how two observers will mirror each other's experience.

Article A diagram of the Special Relativity relationship

I've also addressed your question of how relative motion can be reconciled with accelerations here:

https://www.researchgate.net/publication/293477077_The_Twin_Paradox_Resolved

I believe there remains a contention between us (as with Oliver) of what conditions will be like for a falling object as it reaches an event horizon. That is the same elevation where light is unable to escape going in the opposite direction, i.e., extreme, where the falling object would have accelerated to a velocity of c and have an infinite mass. I can't see out matter could continue to exist as-such at that elevation.

Oliver, I am mystified by your contention that measures of distant accelerations and velocities are problematic because they "are locally measured quantities." Astronomers make such measures of distant objects on a regular basis, apparently unaware of your concern. Conceivably, an astronomer could make such measure of a distant phenomenon both from earth and from a distant space probe; the latter would not be local, but would be expected to be in agreement.

James, your mystification is caused by not taking into consideration that the velocities you have mentioned and astronomers have measured are of such a kind so that we can easily take a flat spacetime as a premise, and curvature effects can be ignored. Therefore, velocities of remote objects like stars or some nearby galaxies can be "measured" (better:extrapolated) by leveraging the affine connection.

Things are already getting much more complicated when talking about the "velocity" of a distant galaxy or a quasar.

That's fine. An astronomer can in principle observe an object falling into a black hole perpendicular to her line of sight and confirm that the object accelerates to the event horizon. No problems of locality.

James, you just continue denying that measuring velocity is a local conecpt. I keep on telling you that you are wrong. I don't think we are really making progress here. Is there any chance I can convince you of that?

In my opinion, this is basic textbook knowledge of general relativity, nothing advanced. I could refer you to those classics of course, but that would seem cheap to me. Just tell me if I should go on trying to explain, but I am really running out of ideas here...I can only reiterate what I have already said. Maybe someone else has a better clue how to convey the message...

Tell me one thing: in your example of an infalling object perpendicular to the line of sight to the asymptotic observer: will you see the object entering the horizon in a finite time, yes or no? If no, then please tell me your exact definition of velocity and of acceleration. Maybe we are just talking past each other...

Dwight: coming back to your posting: general relativity is of course not sufficient to explain the fate of massive bodies falling into the black hole, for several reasons:

- depending on the black hole mass parameter, tidal forces can be quite strong and will sooner or later disintegrate the body, either outside the horizon, or inside only when it cannot be observed any more

- taking into account semiclassical effects as a precursor to a quantum theory of gravity may very well lead to the very non-existence of a horizon in the first place. This is completely uncharted terrain of course.

Therefore: when making predictions and statements, it is always necessary to make clear what the scope of the theory is and what is taken into account, and what is neglected.

Oliver

Forrest Noble

Black Hole theory IMO approaches the limits of General Relativity (GR), as does the beginning of the universe in Big Bang theory. In stellar black-hole theory stars collapse into a type of zero dimensional singularity state when their mass is roughly equal to at least three solar masses, where close to the stars original mass-equivalence is maintained by the Black Hole as a singularity.

As in the case of a beginning singularity in big bang theory, General Relativity also break down IMO in models where black holes are non-dimensional entities. The proposals of non-dimensional entities would accordingly be an escape from reality. Mainstream mathematical black hole theory follow this rationale and are likely a fantasy IMO as well as any of its conclusions related to its theoretical physics. Steven Hawking was a purveyor of such theory and related mathematics.

In my related model there is a presently unrecognized state of matter more dense than a neutron star. Some have proposed a quark model for this black hole state. IMO quarks are not real particles, but the dimensions of the quark state of matter that have been proposed seem closer to the actual size that I believe are the minuscule dimensions of a stellar black hole.

From a premise of a minuscule rather than dimensionless state of matter, better insights into reality might be proposed, as well as new and hopefully better verbal logic as well as new theoretical physics , necessarily an aside from GR, that might have better predictability than dimensionless GR proposals.

Oliver, I've given you examples of how astronomers routinely measure distant velocities, and specifically, how an acceleration of a body falling toward a black hole can be measured from afar. You've simply reiterated that such things can only be done locally. I continue to be mystified. So yes, we seem to be at an impasse.

Would I claim to be able to see an object entering an event horizon in a finite time? Yes, assuming it has come under the influence of the black hole at a fatal distance. Why? Because the idea of a slowing of infall is based on a fundamental confusion of clock-speed with acceleration. You want "my exact definition" of velocity and of acceleration? That feels patronizing. With Relativity, uniform velocity is of course relative, and both conform to the limit c, but otherwise, my definitions are conventional, and consonant with the routine assumptions and work of astronomers.

Regarding your point addressed to Dwight, regardless of the size of the black hole, the event horizon is a place where light going "up" is brought to a halt; consequently, we can be sure that it is just as severe an environment for bodies going "down." For matter to enter that region it would be accelerating at c, with infinite mass, an impossible status, indicating that the transit must involve the annihilation of matter.

James,

"Would I claim to be able to see an object entering an event horizon in a finite time? Yes, assuming it has come under the influence of the black hole at a fatal distance. Why? Because the idea of a slowing of infall is based on a fundamental confusion of clock-speed with acceleration."

I don't know what a "fatal distance" is. This is non-physics jargon. Are you sure you know what you are talking about? Also, the question is clear enough not to cause confusion. As an asymptotic observer you just need to look at your watch and press "stop" when it has happened.

"You want "my exact definition" of velocity and of acceleration? That feels patronizing. With Relativity, uniform velocity is of course relative, and both conform to the limit c, but otherwise, my definitions are conventional, and consonant with the routine assumptions and work of astronomers."

You are being evasive: instead of complaining about me being patronizing, which I am not, because my question is a perfectly valid one, you could just try to maintain a scientific discourse.

Have you understood what I was explaining about velocity "measurement" in Euclidean space which is what atronomers mainly do, even for nearby galaxies?

Sorry James, I am claiming you have not understood the basics of general relativity, as somebody else already insinuated. Instead of claiming all others and all textbooks are wrong, you really should consider reflecting your own knowledge.

This discussion is pointless, which is why I am bailing out now. Please go on without me, I am sure you will manage.

Yes, I think we should avoid each other.

Instead of maintaining that textbooks can't be wrong you really should consider reflecting on your own allegiance to old-school conventions, and how that has worked out in the history of science.

"I don't know what a 'fatal distance' is. This is non-physics jargon. Are you sure you know what you are talking about?" A fatal distance would of course be a distance where an object has been captured by a black hole and extraneous influences would be of no avail. Metaphor -- sometimes clearer and more economical than esoteric jargon, although it may alert a specialist to an intruder.

Your arrogance and dogmatism beg an equally frank response: An aversion to metaphor is an indicator of an absorption in fixed thought-patterns, the sort of fixity that could prevent someone from recognizing the obvious difference between the relativistic slowing of clock-speed and accelerated motion, the sort of fixity that can compel unrestrained diversions.

Hah! You are one of these Vixra guys: http://vixra.org/author/james_arnold

Good, that explains it. I should have noticed earlier. Good bye.

Answers on this question seem to have run their course, having achieved at least some agreement that there can be no gravitational deceleration of an in-falling body at the event horizon of a black hole.

But unscientific thought and behavior has been particularly egregious and annoying here, and I believe it might at least be helpful for improving the general tenor on ResearchGate to point out what has been inappropriate and counterproductive.

It shouldn't need mentioning that ad hominem ridicule is not only offensive but unscientific. If someone believes a question is not legitimate, or that a questioner is not responding to legitimate answers, that can be simply stated, after which further involvement in the discussion is unnecessary, and persistence can even constitute harassment.

Citing authority or consensus in an attempt to refute a question is not just unscientific, it is dogmatic by any standard, in any field. Scientists, especially professional scientists, should be fully aware that no belief, theory, or principle is above question, and a defense of or against an idea based on credentials or doctrine is only appropriate within a free religious community.

Diversionary answers and irrelevant counter-questions are an indication of resistance based on a feeling of threat, or weakness, and may sometimes be based in a general dogmatism. I've been especially disturbed here by the introduction of the principle of locality in general relativity. Given that it has no bearing on whether bodies falling toward an event horizon accelerate or decelerate, and given the strident way it has been introduced and repeatedly insisted upon, it seems clear that the intent has been somehow unhelpful if not willfully diversionary.

If this is the last entry here, thanks to everyone who has contributed or at least read the question

Ioannis Hadjidakis

Time, Space and all the derivative terms (like velocity) have been mixed up by Relativity Theories and - unfortunately - is rather difficult even for "experts" to follow an argument to its wholeness. It is not Mathematics the guilty, but Physics itself that found to Mathematics an easy way to liberate itself from physical reality and follow the slippery road of imagination.

In offline discussions it has become clear that some mathematics is needed to clarify a confusion regarding the fall of a body toward the event horizon of a black hole.

It is common knowledge that a body falling in a gravitational field will accelerate toward its center of mass. But somehow it is widely thought among black hole theorists that in the extreme case of a fall toward a black hole the acceleration will appear to an observer to “freeze” (stop) at the event horizon.

The Lorentz Transformations deal with increases in motion limited by the speed of light (c). The transformation which gives the clock-speed (t’) of the falling body in relation to that of the observer (t) is: t’ = t√(1-v2), with v being the instantaneous velocity treated as proportional to c. (This treatment of v allows a simplification of the standard v2/c2, which relativists find curiously unobjectionable).

Consider two examples of gravitational accelerations that reach 10% and 90% of c, expressed in terms of a Lorentz Transformation:

At 10% of a body’s acceleration to c,

t’ = t√(1-0.01)

= t√0.99

= t * 0.995

meaning that the falling body’s clock is ticking 0.995 as fast as the observer’s at that moment.

Continuing its descent, when the falling body’s acceleration increases to 90% of c,

t’ = t√(1-0.81)

= t√0.19

= t * 0.436

At an acceleration to .99c, the falling body’s clock-speed is only 14% of the observer’s. When the horizon is reached, the fall accelerates to c with a clock-speed of zero. Thus, no matter how extreme the approach to a center of mass, even an approach to the event horizon of a black hole, it is only the clock-speed, not the fall, that is observed to slow or "freeze."

Biswajoy Brahmachari

Observational evidences of the existence of Black holes are still indirect. They are,

Detection of gravitational waves which have originated in black hole merger.
Measurement of proper motions of stars near the center of Milky way. Since 1995 the motion of 90 stars which are orbiting a supermassive object (called Sagittairus A radio source) have been reported. See:https://arxiv.org/pdf/0903.1105.pdf
Accretion of matter into gravitational potential well of the black hole, and corresponding electromagnetic radiation. See: http://www.spacetelescope.org/news/heic1116/
Study of X ray binary stars (Very first evidence of a blackhole called Cygnus X1 was reported from such a study in 1972). See: http://adsabs.harvard.edu/abs/1975ApL....16....9S

Black holes are supposedly not just mathematical objects which remain in the pages of books of cosmology, they are potentially real objects awaiting a major observational breakthrough.

I agree, the evidence for black holes is indirect, but it's necessarily so, due to their nature. I can't imagine what sort of direct observational breakthrough could ever be possible.

The problem as I've stated it is just that the current model is built on mathematics derived from flawed physics.