The jets are not coming from the black hole per se. They are coming from the infalling material that surrounds the black hole (the accretion disk). As it gets close to the black hole, it heats up, ionizes, and rotates ever more rapidly. This creates strong magnetic fields which then accelerate the ionized material. All this happens _before_ the material falls into the black hole.

Thank you for the explanation. I think this phenomena should occur at a certain distance away from the center of the black, otherwise there would be no more particles to "tell us the story". Yet some astronomical observations show these jets coming out from the center of the black hole and, which really freaks me out, is that the jet is forming from BOTH sides of the plane containing the black hole! And this raises yet another question: If something gets inside the black hole, where does it go?!

I don't think there are observations that tell you that these jets are coming from "the center of the black hole". Black holes (or rather, the event horizons associated with black holes) are incredibly small. For instance, the Schwarzschild radius of the Sun is only about 3 km. (For the Earth, it's only a centimeter!) Even for supermassive black holes, the size of the event horizon is at most comparable to the size of the inner solar system. Compared to the size of the accretion disk, the black hole is just a tiny point in the center. So yes, of course the jets will appear to be coming from "the center", but we are still talking about distances that can be many times the Schwarzschild radius of that black hole. So no, the jets are absolutely not coming from within the black hole itself, just from its vicinity.

As to your second question, as seen by a distant observer (i.e., us) material that falls into the black hole never really crosses the event horizon. If you had a powerful enough telescope that could see very long wavelength light, what you'd see is that as stuff falls, it will appear to fall ever more slowly (and light from it would appear to be redshifted ever more dramatically). Eventually, all the falling would appear to grind to a halt near the horizon, but you'd not really see it, as all light coming from it would become infinitely redshifted and thus undetectable.

So from our point of view, nothing ever really falls into a black hole, stuff just freezes and becomes undetectable near the horizon. In fact, we don't even see the horizon form in a finite amount of time.

Things are different from the point of view of an infalling observer. That observer, once he crossed the horizon, could not avoid falling towards the singularity. But the location of the singularity would not so much be a spatial location but a temporal one: it will be in the infalling observer's finite future, regardless of what path he chooses (in fact, the more the observer accelerates to avoid the singularity, the faster he reaches it; the path with the longest proper time would be the freefalling path.) As the observer gets closer to the singularity, so does other matter, so eventually the observer would find himself in a cloud of extremely hot and dense gas. So hot and energetic, quantum effects could no longer be ignored. What actually happens, then, depends on how extreme gravity and quantum physics relate to each other, which is just a fancy way of saying that we don't really know since we don't have a generally accepted, viable theory of quantum gravity.

V. Toth you raise an interesting question. You state from the point of view of a distant observer, an object can never crosses the event horizon, but stays outside forever (or until the black hole evaporates from Hawking radiation, whichever comes first). However, you also state that from the point of view of the object, the event horizon is easily crossed in finite time (i.e., before the black hole evaporates).

How can reality be so completely different, merely based on the location from which it is observed? It seems that either the object crosses the event horizon or it does not.

Perhaps my question could be better stated:

For the distant observer, the logical sequence of events is:

black hole evaporates before object can cross event horizon.

For the object, the logical sequence of events is:

object crosses event horizon before black hole evaporates.

These seem irreconcilable. Do you have a solution?

This is an extreme situation in relativity. If you take a world line that intersects the event horizon, the proper time along that world line will be finite. (This is the fancy way of saying that an infalling observer will measure a finite amount of time before he reaches the horizon.) For an outside observer, the light cones emanating from the infalling object as it approaches the horizon will take longer and longer to intersect the external observer's world line. As the infalling observer gets infinitesimally close to the horizon, the time it takes for that light cone to intersect the outside observer's world line will stretch to infinity. So no outside observer will ever see the moment of crossing the horizon; this moment will forever remain in their future infinity. And no, outside observers won't exactly see black holes evaporate either, because they have yet to see the horizon form in the first place... and that takes an infinite amount of time for them. This stuff is well explained in books like MTW (Misner's, Thorne's and Wheeler's famous textbook on relativity) and it can be well illustrated using Penrose's conformal spacetime diagrams.

Thanks for taking time to respond. But I did not see an answer to the question. It is a simple question, you would think there would be a simple answer.

BTW, I did read through the explanation in MTW. I did not think the answer they gave was correct, for the reasons stated here: http://www.ptep-online.com/index_files/2011/PP-24-15.PDF.

I did answer your question by stating that the events you describe (the forming of the horizon, and any possible evaporation that may take place afterwards) are never seen by a distant observer in the first place, so it is kind of pointless to discuss the order in which they will not be seen. Having said that, since black hole evaporation takes us beyond classical gravity, one may speculate that in a viable quantum theory of gravity, these infinities are tamed, and (some kind of) a horizon is seen forming by a distant observer; in that case, that observer would also see infalling matter cross the horizon and, of course, any evaporation of the black hole will take place afterwards, so the sequence of events will not change between the two observers.

I am confused...as a distant observer, I never take my eye off of the object heading towards the black hole. It would take an infinite time for the object to reach there, so I can always see a distance between the black hole and the object. The object does not last forever (even protons have a half life), so I can see the object evaporate while it is still a measurable distance from the event horizon of the black hole.

For clarity, let me repeat, what I observe.

1. I can see that the object does not reach the black hole in finite time.

2. I can see the object evaporates (as all things do) in finite time.

3. I can see the object evaporate when outside the black hole.

These are all things I can observe. Now how can you say the object crosses the event horizon.

The object may not last forever but we never even get close to this being of concern. Keep in mind the extreme gravitational redshift. As you watch a clock attached to that object, it will tick ever more slowly. Suppose an infalling observer crosses the horizon at exactly 12 PM according to his watch. You are watching this infalling observer from a safe distance. You keep watching for a billion years... and he is still outside the horizon and his watch is still showing a tiny fraction of a second before 12 PM. This is what I was alluding to in my previous reply that the relativistic effects here are extreme: What is a finite amount of proper time for the infalling observer will amount to an infinite amount of proper time for the distant observer. So no, you don't see #2 and #3. (By the way... we don't know for sure if protons have a half life. Observationally, we only have lower limits on the proton half life. But that has nothing to do with this thought experiment, since in the comoving frame of the proton in question, not much time passes.)

But I do see #2 and #3, at least in my thought experiment. Let me explain.

It is estimated that the half life of a proton is 10^32 years. The object is made of reflective material. The distant observer waits 10^32 years, and then shines a flashlight at the object. Light travels faster than the object, so the light will overtake the slower moving object and the reflected light will bring back to the observer the information that even after 10^32 years (plus light travel time there and back again) the object is still outside the event horizon--at least the remnants of the object. The distant observer can continue to periodically shine a light and get back a status report until even the remnants have disintegrated.

What is there not to observe?

I don't want you to think I ignored your comment on proton half life, so let's assume the object is indestructible. The black hole, however, evaporates after 10^100 years.

The distant observer in this case waits approximately 10 ^100 years and shines the flashlight at the observer. The distant observer's timing is impeccable, and the light beam arrives at the object five minutes (according to the distant observer's watch) before the black hole evaporates and the event horizon disappears. The light returns to the distant observer with the information that the object is still outside the event horizon. Five minutes after the first beam, the distant observer shines another beam and this time the status report is that the object is still there but the black hole is gone.

All calculations for the thought experiments are integrals performed with the Schwarzschild metric.

Actually, your light will not overtake your slower moving object. From the distant observer's perspective, that beam of light will also appear to slow to a crawl near the event horizon. There is what is called the "horizon of last influence" (again, read your MTW!) beyond which any light a distant observer shines on the infalling object will not reach that object before the object crosses the horizon. So even though you will never see the infalling object cross the horizon, there will be a moment in time after which you can no longer influence the object in any way, including bouncing photons off it, and watch the result.

As to black hole evaporation, that is a quantum phenomenon. Once you allow quantum physics into the picture, all bets are off as we don't have a viable theory of quantum gravity. Perhaps the horizon is fuzzy. Perhaps the horizon forms in a finite amount of time. Perhaps there is a "firewall". There are plenty of papers out there arguing all sorts of exotic things, but as I said, no viable theory, no consensus, and certainly, no observational evidence.

I have read MTW. I refer you again to : http://www.ptep-online.com/index_files/2011/PP-24-15.PDF.

Here you just have your facts wrong. According to the Schwarzschild metric, light will always overtake matter free-falling towards a compact mass--no matter how much of a head start is given. The horizon of last influence simply has nothing to do with this straightforward calculation. You don't even have to do the calculation, just think about it for a minute.

The Schwarzschild metric teaches us two important facts that you accept:

1. From the distant observer's perspective, matter cannot reach the event horizon in finite time.

2. Light travels faster than the free falling object.

What I have stated above is the inescapable logical result of these two facts.

You are simply disbelieving the results of calculations that one can easily make.

Let me respond to your comment on black hole evaporation and quantum effects.

The thought experiments above indicate that matter cannot cross the event horizon of a black hole. This is inevitable, given that in GR energy and momentum are conserved (see A. Einstein's 1916 paper "Hamilton's Principle and the General Theory of Relativity", or for a more recent discussion, see http://www.ptep-online.com/index_files/2011/PP-24-14.PDF )

But if matter cannot cross the event horizon of a black hole, then black holes never form. That is, the last particle on the surface of a collapsing star will never be able to cross the Schwarzschild radius to form a black hole. Black hole evaporation and quantum effects are simply physical phenomena that never happen. They are irrelevant.

This puts us in a better position to answer Ali's original question. If matter does not compact below an event horizon to become a black hole, what happens instead? Why are there jet emissions? Here is what I suspect.

Gravity is an amazing magnifier. Instead of using optics (like a magnifying glass) gravity uses time. Imagine our object is part of the surface of a collapsing star. The background radiation that to a distant observer takes billion years to reach the object, in the object's perspective is focussed by gravity to arrive instantly. Any fusion reactions on the surface of the collapsing star that appear to the distant observer to take billions of years, cumulatively occur instantly at the location of the object. Just imagine the incredible focused inferno resulting from this crucible created by gravity. Tremendous releases (burst of light, explosions casting out matter) could be expected in this mixture. I suspect this is the source of the jet emissions we observe.

There are a couple of other things in play here as well, that deserve more explanation that this forum allows. But I will throw them out anyways.

One is that as the components of the energy of the gravitational field increase, the components of the energy of matter decrease. Again see Einstein's 1916 paper, "Hamilton's Principle and the General Theory of Relativity", equation (21). This suggests that in strong gravity fields matter becomes more unstable.

Finally, any vaporization of matter at the surface of a collapsing star will diminish the escape velocity at the surface (this is because with loss of mass at the surface, the Schwarzschild radius will retreat faster than the radius of the volume of the collapsing star). The result is that any burst of activity at the surface that quickly removes mass, will also release less dilated views of activity at the collapsing surface. This is an explanation for the sudden bursts of light from quasars.

Douglas, what I was trying to say is that the light ray will not overtake infalling matter before both hit the horizon. Thus, the overtaking will never be seen by distant observers. Again, you said you read your MTW; I refer you to chapter 33, pages 873-874 where and the subsequent discussion on the concept of the surface of last influence (I mistakenly called it "horizon of last influence" in my preceding post; I blame misfiring neurons.)

What you are stating is a fallacy; a misunderstanding of how general relativity works in the extreme environment near an event horizon. The easiest way to see this is to draw appropriate diagrams, in particular Penrose diagrams with the world lines of the infalling object, the ray of light, and the distant observer. Then you will see that neither the ray of light nor the infalling matter will ever be seen as reaching the horizon by a distant observer; and depending on when they were emitted, rays of light may or may not cross the infalling matter's worldline before both hit the horizon. Importantly, after a certain moment in time, the distant observer can no longer aim a beam of light at the infalling matter in such a way that their worldlines cross outside the horizon.

As to your speculation about the jets near a black hole, all I can say is that if you can prove it with properly derived mathematics, publish it in a reputable journal. Using the answer feature on ResearchGate is probably not the best forum to promote unconventional, maverick, unproven ideas. Here, we should do our best to actually answer the question posed by the questioner. In this case, I was trying to focus on the concept that whatever the physical mechanism might be behind the jets, they're not coming from the black hole proper, but from its immediate vicinity, namely the accretion disk.

I read again 873-874 of MTW. The trick here is that Salvatius is using ingoing Eddington-Finkelstein coordinates to make calculations. If Salvatius used the coordinates of the distant observer, the results are what I describe above.

Using Eddington-Finkelstein coordinates essentially begs the question as to whether the event horizon can be crossed. Salvatius is assuming the Eddington-Finkelstein coordinates can cross the event horizon, and on the basis of this "proves" the collapse of the surface across the event horizon. But the assumption is wrong. The Eddington-Finkelstein coordinates never cross the event horizon. They are unable to. You can easily show this by using the coordinates of the distant observer to track the progress of the Eddington-Finkelstein coordinates towards the event horizon. All this is discussed in the reference I gave you, http://www.ptep-online.com/index_files/2011/PP-24-15.PDF.

As far as your other comments, except for the one post where I made some speculations on where jets come from, etc. (and who had done more than speculate?), I have stuck very close to the safe harbor of what can be easily demonstrated using the Schwarzschild metric.

Douglas, the concept of the surface of last influence is not dependent on the choice of coordinates. Again, it can be easily seen by drawing Penrose diagrams.

The surface of last influence is dependent on choice of coordinates. It does not exist from the perspective of the distant observer. That is why MTW had to use ingoing Eddington-Finkelstein coordinates to draw it. Any, I repeat, any, diagram that shows the event horizon is crossed, is based on coordinates that themselves are assumed to cross the event horizon. You must beg the question to get across the event horizon.

From the perspective of any and every coordinate system that remains outside the event horizon, it is impossible to reach the event horizon in coordinate time. This is fundamental in the Schwarzschild metric. If you need more information on this, I would be glad to give it to you.

This may be too simplistic for you--but here is an explanation in layman's terms why changing coordinates does not make the impossible possible. http://www.noblackholes.com/coordinate_pathology.html

Douglas, you keep providing as references your own writings, which seem to question established theory. I assure you, the surface of last influence is most certainly not dependent on the choice of coordinates. Again, I implore you to try and draw a (coordinate-independent!) Penrose diagram with an infalling world line, the world line of a distant observer, and world lines representing rays of light emitted by that observer and reflected by the infalling object.

Actually, never mind, I just drew a Penrose diagram (I hope it uploads properly) that shows the surface of last influence. What should be clear from this diagram is that:

1. Proper time along the world line of infalling matter is finite. As measured by his own clock, an infalling observer would reach the event horizon in a finite amount of time.

2. An external observer will not see the horizon form, or anything (matter or light ray) cross the horizon in finite time. Any light rays coming from the horizon will intersect the world line of a distant observer at future infinity, or never.

3. Once an observer crosses the "surface of last influence", any rays of light emitted by the observer will not intersect the world line of infalling matter before crossing the horizon. Consequently, no reflected light can ever reach the distant observer.

My understanding of understanding of Penrose diagrams is that they are based on Kruskal coordinates. Kruskal coordinates cross the event horizon.

You are welcome to correct me if I am wrong.

For a basic introduction to Carter-Penrose diagrams (not my writing) see

http://www.ift.uni.wroc.pl/~blaschke/master/Felinska.pdf

I don't mean to be abrupt, I greatly appreciate the time you are spending on this. And the drawing was very nice. But without the use of Kruskal coordinates (or similar coordinates that cross the event horizon), Penrose diagrams could not traverse an event horizon. The Schwarzschild metric, once you understand it, is not that complex an equation. It is undefined inside the Schwarzschild radius. You have to monkey with the equation to get inside the Schwarzschild radius. Normal rules of math simply can't get you there.

The topological relationships that are evident in a Penrose-diagram are not dependent at all on the choice of coordinates.

Penrose diagrams are simply a convenient representation of the topological relationships between world lines, horizons, and other events. Penrose-diagrams are not based on Kruskal-Szekeres coordinates (which are specific to the Schwarzschild solution) though in the Schwarzschild case, they are indeed similar to Kruskal-Szekeres diagrams. (But not identical; Penrose diagrams are much more radical, in that they map spatial and temporal infinity at a finite distance from the origin in the diagram. Since the mapping is conformal, however, the angle of light rays in the diagram is preserved; rays of light always travel along 45 degree lines.)

WIthout exception, the literature I looked at claimed the Penrose diagrams near the Schwarzschild radius were based on the Kruskow coordinates or some close variation.

For example, in the reference I sent you (http://www.ift.uni.wroc.pl/~blaschke/master/Felinska.pdf), the coordinates of the distant observer used in eq. (22) are discarded near the Schwarzschild radius, because they do not allow the event horizon to be crossed. So they used EddingtonFinkestein coordinates to get through the event horizon. Then they build the Penrose diagrams using Kruskal coordinates. This allows them to move the singularity to r=0.

Same thing here: http://www.math.unb.ca/~seahra/resources/notes/black_holes.pdf. A close variation of the Kruskal coordinates are used.

I am looking at your Penrose drawing. I see the same thing. Looks like Kruskal coordinates, or a close variation to me. The singularity has been moved to r=0. If the distant observer were used in the diagram, the singularity would be at r=R.

The travelling observer in your Penrose diagram crosses the surface of last influence at the same time the infalling matter crosses the event horizon. At this point, from the perspective of the distant observer, both the travelling observer (if Kruskal coordinates or a variation) and the infalling matter simultaneously violate the limits of the Schwarzschild metric. They cannot detect the violation, because they both go through the violation (singularity from the perspective of the distant observer) together. From the perspective of the distant observer (not shown in your diagram) both the traveling observer and the infalling matter are in violation of the limits of the Schwarzschild metric. They are no longer within defined regions of the Schwarzschild metric, that is, they are in violation of the laws of conservation of momentum and energy defined by the Schwarzschild metric and by GR.

The use of co-moving coordinates, in my mind, is bogus. I can just as easily find coordinates that co-move with a particle as it breaks the speed of light and goes all the way to infinity. You won't detect the particle going through the singularity in the Schwarzschild metric at v=0 because the particle and the observer will go through the singularity at the same time. This boot strapping defeats the physics part of GR. The limits in the Schwarzschild metric (v=c for velocity, r=R for gravity) are there to represent real physical limitations. For gravity, these limitations are based on Einstein's view of the conservation of momentum and energy in correspondence with the Hamiltonian Principle. This is absolutely central to his theory of GR. See the Einstein paper I cited previously, eq. 21 (not my writing).

While I have no gripe with theoretical physicists coming up with theories, they need to be honest with the public. Black holes violate Einstein's theory of GR. Just admit it, and then come up with some legitimate theory other than GR to justify the belief that black holes form. But it is disingenuous to claim black holes are based on GR while doing these mathematical shenanigans. I especially take offense at the claim Einstein was "wrong" when he said black holes did not conform with GR. This is just not right. Einstein was right about black holes and GR. But GR has just been replaced with something that looks nothing like Einstein's theory.

Personally, I think Einstein's theory of GR and his view that black holes don't form better fits the observed data (e.g., jet emissions etc.) and just makes more sense. It is also intellectually satisfying.

You have been very patient and gracious. I don't want to take more of your time and invite you to bow out any time. Thanks again for the discussion. I enjoyed the chance to discuss the issues. (I am also looking for opportunities to pull people out of the matrix, so will welcome other opportunities to address these issues)

Oops, I meant the singularity in the Schwarzschild metric at v=c.

My apologies for the extended discussion. Time to let this one go.

Just a casual observer, I have to ask: when does accreted mass-energy become bound to the accreting object? If binding mass-energy released by disintegrating nucleons becomes bound to the accreting object, even if its time freezes before it can cross the event horizon, doesn't it contribute to the accreting object's total mass? In this case mustn't the dimensions of the event horizon increase, eventually encompassing newly accreted mass-energy 'shells'?

Not sure what you mean by "bound to the accreting object", but any mass-energy that crosses the event horizon (in its own proper time; of course it'll never be seen crossing the horizon by a distant observer) will contribute to the mass and, therefore, the event horizon radius of the black hole. And yes, as the radius of the horizon increases, it means that other bits of infalling matter will intersect it sooner. Just to be clear, the jets that this question was originally about form before any of this happens, as material in the rotating accreation disk is accelerated.

V. Toth,

Thanks - to be clearer, I hope, at what point does mass-energy contribute to the total mass of the black hole? If infalling mass-energy appears to a distant observer to be frozen outside the event horizon, mustn't it still be considered to contribute to total BH mass? Can a distant observer then (in terms of relativity, at least) detect the 'disappearance' of subsequent infalling mass-energy occuring at the new, expanded event horizon boundary?

In this scenario, can't a completed black hole be identified by a distant observer? As I understand, physical evidence of relativistic jets, corona and accretion disk are observed - I think indicating that a BH has indeed formed.

Moreover, as I understand, the velocity of polar jets is related to the escape velocity (indicating total mass) of the compact object accreting mass-energy. Relativistic jets are only likely to be produced by objects whose escape velocity at least approaches c.

I agree wholeheartedly that relativistic jets do not expel any mass-energy from within the event horizon! IMO, only fundamental particle residue resulting from material disintegration at the event horizon (i.e., firewall) can be accelerated to relativistic velocities...

The distant observer never sees the horizon form. He would, however, see the accumulation of mass and could deduce that a horizon is in the process of forming (even though the process will not be seen completing in a finite amount of time) and could also estimate the total mass that is contributing to the forming horizon. And even though a fully formed horizon is never seen, infalling mass-energy would, for all intents and purposes, vanish (i.e., any light from it would be exponentially redshifted and thus no longer detectable) so what the distant observer sees is a massive, compact, dark object... and the physical processes (accretion disk, jets, etc.) associated with this compact, dark object will be the same, horizon or no horizon.

Douglas,

It is true that a distant observer will never see in-falling matter reach the event horizon, let alone the formation of an event horizon in the first place. I have failed to find any explanation as to how current black holes could exist with respect to distant observers if an infinite amount of time is required in regards to their formation. Others support this side of the debate such as Abhas Mitra (http://www.nature.com/nindia/2009/090511/full/nindia.2009.130.html). One can easily take the position that the finite amount of proper time required by in-falling matter originates from the local clock ceasing to evolve, i.e. external processes occur faster and faster due to internal time intervals becoming increasingly small. Such events therefore never actually occur, but are an illusion due to time dilation for in-falling observers. Change of coordinates is related to this perspective because the vast majority mix space and time components to remove coordinate singularities.

To make matters worse, relativistic jets are not only observed from black holes. Neutron stars for example also have relativistic jets, some of which are not accompanied by accretion disk. Several models (GRB) can produce relativistic jets from within the stellar mantle due to internal magnetic fields, although this is not extended to objects with event horizon. With my own treatment of general relativity on a per particle basis, event horizon never form without infinite energy. These features appear to originate from the simplicity of Einstein’s field equations, where the effects of individual particles are abandoned in favor of accumulative mass or mass/momentum densities. It would therefore be possible for relativistic jets to originate from within objects assuming they do not have event horizon. In fact, observations have depicted jets originating much closer than expected with respect to theoretical treatments (http://web.mit.edu/newsoffice/2004/blackhole.html). The existence of event horizon and mechanisms behind relativistic jets are still up for debate, as there have been no direct observations sufficient to sway the conclusion either way.

Michael,

Well put, however, in regards to your conclusion "I have failed to find any explanation as to how current black holes could exist with respect to distant observers if an infinite amount of time is required in regards to their formation"

- the evidence of BH existence, even if indirect, that seems to conflict with BH (event horizon) formation theory strongly suggests that the theory is incorrect, or at least incorrectly interpreted.

This is why I'm motivated to suggest a mechanism allowing the accretion of BH mass external to an event horizon - allowing the creation/extension of an event horizon subsequent to mass-energy accretion. This may involve quantum 'firewall' conditions that are not considered in relativistic theory. Again, see http://physics.aps.org/articles/v6/115 - its subheading states:

"New theoretical work rekindles the question on whether black holes have an interior: Would a firewall destroy any observer crossing a black hole horizon?"

It also offers a free link to the recent letter by Donald Marolf and Joseph Polchinski published in Phys. Rev. Lett. 111, 171301 (2013): http://physics.aps.org/featured-article-pdf/10.1103/PhysRevLett.111.171301.

James,

I'm unsure of what the consensus is with respect to these conflicts, but the formation and growth of black holes are derived in a frame of reference that is not observable by distant observers. It would therefore be impossible for current “black holes” to be those as described by Einstein’s field equations. Abhas Mitra’s work is similar to the black hole firewall theory, but without an event horizon. The term given to these is eternally collapsing objects (ECO); however, there is a much simpler answer in regards to the nature of black holes. These objects likely consist of dense quark matter in the color superconducting state. Such conclusion can be reached by applying classical physics to the foundations of general relativity without the additional assumptions made by Einstein’s field equations; i.e. by applying general covariance, time dilation, the space-time metric and per particle solutions.

One method I’ve proposed for verifying the validity of Einstein black holes is through the direct detection of gravitational waves. Although gravitational waves are not directly related to the nature of black holes, a null result would clearly rule out Einstein’s field equations and any similar theory. Over the past 10-20 years the expected (theoretical) rate of gravitational waves has decreased by several orders of magnitude (1000x) to compensate for prior null detections. With advanced LIGO becoming available next year, it will soon be clear as to the validity of modern general relativity.

Matter does not come out from the black hole, it comes out from the vicinity of the black hole, within a few Schwarzschild radii. According to the Two Component Advective Flow Model (TCAF) championed by S. K. Chakrabarti and his collaborators, the flow in the accretion disk feels a barrier due to a Centrifugally Supported Boundary Layer, so called CENBOL, and this barrier helps in the collimaiton of the jets due to the unbalanced thermal gradient force.

Michael,

"These objects likely consist of dense quark matter in the color superconducting state."

I can't assess - is there some basis for expecting any quark material's degeneracy pressure to resist the continued collapse of billions of solar masses?

IMO, the progressive structural decomposition of matter in the production of increasingly dense collapsed compact objects, illustrated by white dwarfs and neutron stars, indicates an ultimate collapse of matter would extract its binding mass-energy while expelling its component fundamental particles, requiring dimensional occupancy, as residue. The result could be a dimensionless focal point of persistently contracted (curved) gravitational spacetime.

James,

With Einstein's field equations the degeneracy in stars is limited to up, down and strange quarks. For example, neutron stars are in the hadronic phase while quark stars barely enter the color-flavor locked phase (http://arxiv.org/pdf/0709.4635v2.pdf). For more massive quark flavors, additional pressure is required to avoid particle decay. Supermassive "black holes" would likely have enough mass to produce top quarks at their cores, which are about 1822x more massive than strange quarks; i.e. there is a lot of room for degeneracy beyond what is restricted by Einstein's field equations.

The way that I have rewritten general relativity provides the coordinate deformation for each particle's field depending upon the background field, i.e. the influence due to all other particles in existence. As the energy of a single particle reaches infinity, the localized field (gravitational potential, electric potential, ect.) begins to contract into a coordinate singularity. It would therefore be impossible to create a conical or coordinate singularity in realistic scenarios. Degeneracy simply increases the gravitational potential of each individual particle, implying that the field of composite objects should be dependent upon particle type. Such methods are not possible with Einstein's field equations due to their simplicity. In fact, I do not think this formulation can even be written in terms of a geometric field equation. It requires numerical approximations derived from classical laws and the foundations of general relativity. This is essentially why the direct detection of gravitational waves is crucial, as my theory does not predict them. Metric waves instead play a much more important role in regards to the unified field theory, i.e. particles consist of localized Planck scale fluctuations of space itself. We are getting to the point where the existence of gravitational waves is highly unlikely. For example, enhanced LIGO was initially expected to detect

Michael,

I can't evaluate, but I understood that it was the velocity of collapse that transforms matter into denser forms and that it is the particle's ability to resist further degeneration that prevents further collapse.

http://en.wikipedia.org/wiki/Neutron_star

"In general, compact stars of less than 1.44 solar masses – the Chandrasekhar limit – are white dwarfs, and above 2 to 3 solar masses (the Tolman–Oppenheimer–Volkoff limit), a quark star might be created; however, this is uncertain. Gravitational collapse will usually occur on any compact star between 10 and 25 solar masses and produce a black hole.[7]"

While its not likely that multimillion solar mass black holes are formed in a single collapse, they ultimately may form in the repeated mergers of increasingly dense objects. There is an enormous gap between 10-25 solar mass objects and many million mass objects. If the collapse of a 10-15 solar mass object may exceed the degeneracy pressure of quarks, it seems unlikely that quarks could support a many million solar mass object.

James,

With Einstein's field equations (EFEs), black holes can form through various solar mass conditions. In the modern perspective it would be incorrect to view the formation of conventional black holes in terms of degeneracy. The focus is instead placed upon the degeneracy achievable prior to mass surpassing the limit defined by the Schwarzchild radius. The degeneracy of free quarks is also poorly defined; however, current theoretical attempts allow pressures greater than those achievable through EFEs.

If you were to consider a unified field theory where matter and fields consist of Planck scale fluctuations of space (analogous to a 3-d mass/spring system), it would be impossible to force an infinite amount of energy density into a single region. I define such fluctuations by their energy density (scalar-vector field), which is directly proportional to the gravitational potential of each particle. Furthermore, the background vacuum energy (from all other particles) relative to each individual particle defines the space-time metric. It can essentially be viewed as waves moving through a medium, where the medium is the vacuum energy density from all other localized waves. In this perspective, one does not need to worry about degeneracy because whatever occurs will not result in a coordinate singularity (infinite vacuum energy density). Although I have managed to connect the standard model with gravity, I've yet to finish the unified field theory necessary for predicting exactly what occurs in extreme scenarios. However, I do have a good understanding of what causes gravity, mass, charge and electromagnetic fields.

Michael,

I mention the perhaps standard interpretation - that the collapse of stars ~>25 solar masses exceeds the capability of even a hypothetical quark star to prevent continuing collapse - only as a reference point.

As I understand, free electrons and some protons have been detected in the relativistic jets of supermassive black holes. This suggests to me that some at least nuclear or quantum processes are occurring outside the event horizon. The majority of atomic mass-energy is the bound quark kinetic energy confined within the proton. It seems to me that extracting the majority of nuclear mass-energy would not require the decomposition of quarks - only the disintegration of nucleons. If the mass-energy released was retained as gravitationally curved spacetime, the free quarks could be ejected as residue. In this way an empty shell of frozen spacetime gravitationally curved towards a singular focal point might produce all the gravitational effects of a singularity without requiring any unphysical, dimensionless form of matter.

James,

I'm unsure if the pressure in the core of a 25 solar mass star would be strong enough to overcome quark degeneracy. Current studies limit calculations to up, down and strange quarks as more massive flavors would not be encountered with respect to EFEs. In addition, stars with >40 solar masses have been observed not to form black holes, which is contrary to the current paradigm (http://www.telegraph.co.uk/science/space/7952620/Magnetic-mega-star-discovery-challenges-black-hole-theory.html). However, I am fairly certain that the universe is in a steady state, which would be incompatible with conventional black holes. For example, if the universe has always existed, black holes with event horizon would simply consume everything contrary to observations. Therefore, the validity of conventional black holes can be indirectly determined through several cosmological tests.

Regardless, the mechanisms behind relativistic jets can vary between cases. For example, not all objects have accretion disk requiring material to be ejected from within. Any quark material ejected however would not be free, but in the form of mesons and baryons. These would then decay into elementary particles such as electrons, positrons, protons and neutrinos. Objects with accretion disk will surely propel the material into jets, but this does not rule out magnetic fields originating from the central object rather than in-falling matter; i.e. conventional black holes do not have magnetic fields. Rotating objects in a color superconducting state however have immense magnetic fields due to the London moment. In either case, the jets are powered by magnetic fields and possibly the momentum gained from gravitational potential. I also remember reading about numerical models failing to collimate matter into the observed widths of jets, but I cannot seem to find the source at the moment.

Michael,

The ESO press release contains a much better description of the very peculiar conditions used to derive the estimate of 40 solar masses for the identified magnetar's progenitor. See http://www.eso.org/public/usa/news/eso1034/. It also contains a link to the related research report. I won't question their findings here, but let's assume for the moment that under some conditions such a massive neutron star can exist - that has little bearing on whether a multimillion solar mass quark star could exist.

Yes, collapsing objects do not necessarily have an accretion disk, and I agree that disintegrated quark material would not be free for long - and would soon produce the protons identified in relativistic jets. The production of relativistic jets is an area of active research - for example see http://xxx.lanl.gov/abs/astro-ph/9908283, http://dx.doi.org/10.1088/1742-6596/355/1/012016, http://arxiv.org/abs/1303.3004 and http://arxiv.org/abs/1301.6771.

What seems clear is that it is the black hole gravitation that is the ultimate source of expulsion energy - but the precise mechanism by which accretion disk and black hole rotation, along with MHD effects contribute to particle velocity is not fully understood.

1st comment: As far as I am informed, it is believed that the matter in the jets originates in the accretion disk that circles the supermassive black hole (SMBH).

2nd comment: Regardless the origin of the matter, its escape outward is possible only through the jets that form in the narrow cones, where the orientation of magnetic field is radially oriented, i.e. above the magnetic poles of the central object. The extremely strong magnetic field can be expected due to the plasmatic character of the accretion disk. The common stars should have a static electric charge (the mechanism of the occurrence of such a charge can be found described in the works briefly sumarized in my paper: Neslusan L.: 2001, "On the global electrostatic charge of stars", in: Astronomy and Astrophysics, vol. 372, pp. 913-915). Such the charge should be property of all plasmatic objects, also SMBHs before its collapse and (since the electric charge conserves in the BH) also after the collapse. The charge forces the electrons in the accretion disk to orbit the central SMBH much faster than the protons do. This different speed of the particles charged with the charges of opposite polarities results in the electric current and, consequently, dipole magnetic field.

3rd comment: The recent discovery by Chinesse researcher Ni (Ni, J.: 2011, "Solutions without a maximum mass limit of the general relativistic field equations for neutron stars", in: Science China: Physics, Mechanics, and Astronomy, vol. 54, pp. 1304-1308) indicates that the central SMHB could not be any black hole (i.e. the object with an outer physical radius collapsed in its proper time below the event horizon), but a prosaic cosmic object, with the outer radius in "our" part of the universe. Some mass ejections from the surface of such object would then be possible. So, the mass in the jets could originate directly in the central compact object. (Remark: Compact object is the kind of objects the spacetime of which inside it as well as in its vicinity can be described only by the general relativity. The classical, Newtonian physics is not usable, here, because the spacetime is curved too much for a classical approximation.)

AGN, Jets and assumed SMBH

An active galaxy emits up to thousands of times more energy than a normal galaxy. Most of this energy is released in visible light as well as in all other wavelengths, from radio waves to gamma rays. From the Astrophysical point of view, in order to explain the enormous luminosity of Active Galactic Nuclei (AGN) including Jet phenomena, the investigations of momentum exchange and energy release processes from the vicinity of Compact Stellar Objects - currently believed to be Black Holes - through different possible mechanisms, is a topic of current research in relativistic astrophysics.

Most researchers operate under the hypothesis that all AGN phenomena result in one way or another, from accretion of matter onto, and its expulsion in relativistic Jets from the vicinity of a Super Massive Black Hole (SMBH) in Galactic Nucleus. The general model of matter accreting toward a central SMBH and then ejected from its vicinity through relativistic jets by the action of strong magnetic fields associated with accretion discs, appears to be quite capable of accounting for observed AGN properties.

However, here I show that it is impossible for the matter accreting toward a central SMBH to account for observed AGN properties.

1. Generally the in-falling particles in the accretion discs consist of electrons, ions, neutral particles as well as groups of particles. Strong magnetic fields can be produced by the flow of accreting particles only if all such particles are only electrons or only ions. In a mix of particles, only heterogeneous localized magnetic fields can be produced which can never produce the effects associated with strong uniform magnetic fields.

2. Charged particles moving through a strong magnetic field only experience a Lorentz force at right angles to their velocity vector and hence can never get linearly accelerated to high velocities by the action of such magnetic fields.

3. Any magnetic field produced by the motion of charged particles cannot influence the motion of these charged particles unless it interacts with some external magnetic field.

4. In general, magnetic fields produced by accreting particles in the accretion disc can neither accelerate these particles nor impart high kinetic energies to these accreting particles.

5. The accreting particles in the accretion disc are only accelerated by the gravitational force of the central compact body. Being a motion in central force field, the in-falling motion of the accreting particles is always constrained by maintaining their Angular Momentum constant.

6. Let us assume that a certain fraction of mass of the accreting particles with a total radially inward momentum Pin, is somehow ejected radially outward in the form of a jet, with a total outward momentum of Pout. Then it is obvious from Newton's laws of motion that the central compact body will need to apply a sort of reaction force amounting to imparting an outward total momentum of sum of Pin + Pout to these accreting particles for enabling the ejection of jets. However, such a reaction force can never be provided by any Black Hole since these jets are assumed to be produced from the accretion disc just outside of the Event Horizon, and not from the physical surface of the gravitating body.

7. Further it is well known that gamma radiation can only be produced by nuclear reactions or nuclear interactions. As such Gamma radiation, which is a part of intense non-stellar radiation from AGN, can never be produced from gravitational thermal energy in the accretion disc.

It may therefore be concluded that observed AGN properties cannot be explained by assuming the Compact Stellar Object at the center of AGN to be the fictitious Super Massive Black Hole. In fact it has already been proved that Black Holes are a Mathematical Fantasy, not a Physical Reality.

Article Black Holes are a Mathematical Fantasy, not a Physical Reality

In fact Astrophysicists took a wrong turn in 1926 when R. H. Fowler introduced the fictitious notion of electron degeneracy pressure, derived from Fermi-Dirac statistics, as the pressure that holds up the white dwarf cores from gravitational collapse. This fictitious notion of electron degeneracy pressure has played a dominant role in subsequent developments and led Astrophysics into Black Holes.

Article Stellar Core Collapse Models are Erroneous and Misleading