## If no singularity, what’s inside a big black hole?

 Quote by mesinik Now, let's sit on this ring and push a mirror inside with a stick, beyond the event horizon ...
Good luck to you, because I am not going to be the one sitting on your ring...it would be a decidedly uncomfortable position to be in, I can assure you, what with your brains being sucked out through your toes, all ten of which by the way would have been stretched to the length of a freight train...you get the picture.
Anyway, let's for argument's sake pretend it was possible to do such a thing - you wouldn't be able to see anything reflected off the part of the mirror which is at and inside the event horizon. Also, you would not be able to pull the mirror back out. Basically, this whole thing is a waste of time.

 There is a recent review by Mathur that is very clearly witten and a pleasure to read: http://arXiv.org/pdf/1201.2079 From his Fuzzball viepoint, these questions eg about a singularity are irrelevant.

Thank you for positive feedback. I, too, would say: the points of view of avatar Bernie G might sometimes be a bit unanticipated, but they are fun to read and certainly on the positive side of this pleasant forum.
 Quote by Bernie G I think your example of pushing a mirror inside the event horizon of a large black hole illustrates the sorry state of affairs of contemporary black hole analysis. The Tolman–Oppenheimer–Volkoff equation is normally quoted, and this equation results in infinite pressure inside the event horizon. So as an example, if we consider a 10 million solar mass black hole, the gravitational acceleration at the event horizon would be about one millionth that at the surface of a neutron star. The surface of a neutron star obviously doesn't have infinite pressure.

Dear person behind avatar Markus Hanke
I am pleased to see, my text was interesting for you.
But regrettably (probably my grammar was a bit too heavyish), there is some unnecessary misunderstanding here. I will try to use less grammar next time; but you, too, could you please next time consider reading a sentence from the beginning to the end (and if you don't get the point, then reading again and doing some thinktank work) ... before you try to make fun of it, OK?
Hint: compound sentences include often many parts and you should read all of these parts. You should not cut out 1 little piece and advertise this as the meaning of a compound sentence.

 Quote by Markus Hanke Good luck to you, because I am not going to be the one sitting on your ring...it would be a decidedly uncomfortable position to be in, I can assure you, what with your brains being sucked out through your toes, all ten of which by the way would have been stretched to the length of a freight train...you get the picture.

 Quote by mesinik Dear person behind avatar Markus Hanke Thank you for your attention. I am pleased to see, my text was interesting for you. But regrettably (probably my grammar was a bit too heavyish), there is some unnecessary misunderstanding here. I will try to use less grammar next time; but you, too, could you please next time consider reading a sentence from the beginning to the end (and if you don't get the point, then reading again and doing some thinktank work) ... before you try to make fun of it, OK? Hint: compound sentences include often many parts and you should read all of these parts. You should not cut out 1 little piece and advertise this as the meaning of a compound sentence.
Dear mesinik, I must apologize if you felt offended by my post. Reading through it now, I must admit that it does read a bit like a personal attack on your post, poking fun at it. Please be assured however that I did not actually intend it to be that way; I was merely trying to illustrate that sitting just above an event horizon is just not a possible way to investigate the properties of a black hole. I suppose the style and language of the post got out of hand - entirely my fault.
So again, please accept my public apology. I genuinely did not mean it to come across like this.

 “How can the gravitational acceleration at an event horizon be smaller than at the surface of a neutron star ?” Because gravitational acceleration varies as the inverse of r squared. One of us is making a mistake. I was under the impression that distant super-massive black holes (10 billion solar masses) “disappeared” because the gravitational acceleration at the event horizon is so small (and the curvature so large) that infalling material doesn’t even radiate until it is well within the black hole. Hence I volunteer to sit on the ring and bravely stick my toes inside the event horizon of a trillion solar mass black hole, where the gravity (gulp) should be about as strong as in California. To challange the staus quo even further, here in a nutshell is my minority viewpoint about the size of a star composed of relativistic material inside a black hole: The gravitational energy could be as low as (4GM^2)/(5R) for a typical density profile, or possibly as high as (GM^2)/R (unlikely) if the star has a high density core. The total energy creating pressure would be (Mc^2)/3. Using the viral theorem (the energy creating pressure equals half the gravitational energy), a non-rotating star of relativistic material would have a radius as small as (1.2GM)/(c^2) or as large as (1.5GM)/(c^2), or between 60 - 75% of the Schwarzchild radius. If this model is true, it could be verified someday by the observation of the merger of two approximately equal mass black holes: a massive ejection from the relativistic stars would occur.

 Quote by Bernie G “How can the gravitational acceleration at an event horizon be smaller than at the surface of a neutron star ?” Because gravitational acceleration varies as the inverse of r squared. One of us is making a mistake. I was under the impression that distant super-massive black holes (10 billion solar masses) “disappeared” because the gravitational acceleration at the event horizon is so small (and the curvature so large) that infalling material doesn’t even radiate until it is well within the black hole. Hence I volunteer to sit on the ring and bravely stick my toes inside the event horizon of a trillion solar mass black hole, where the gravity (gulp) should be about as strong as in California. To challange the staus quo even further, here in a nutshell is my minority viewpoint about the size of a star composed of relativistic material inside a black hole: The gravitational energy could be as low as (4GM^2)/(5R) for a typical density profile, or possibly as high as (GM^2)/R (unlikely) if the star has a high density core. The total energy creating pressure would be (Mc^2)/3. Using the viral theorem (the energy creating pressure equals half the gravitational energy), a non-rotating star of relativistic material would have a radius as small as (1.2GM)/(c^2) or as large as (1.5GM)/(c^2), or between 60 - 75% of the Schwarzchild radius. If this model is true, it could be verified someday by the observation of the merger of two approximately equal mass black holes: a massive ejection from the relativistic stars would occur.
I don't really get what you are saying; the event horizon is a boundary beyond which photons cannot escape the gravitational pull of the BH. Its radius is only dependent on the total mass of the BH. As neutrons stars are stable and do not collapse gravitationally, the gravitational acceleration at the event horizon for a BH of equal mass must be much stronger than at the surface of the neutron star ?! If it was the other way around all neutron stars would immediately collapse...

 "the gravitational acceleration at the event horizon for a BH of equal mass must be much stronger than at the surface of the neutron star" I should have been clearer and was referring to a typical neutron star of one or two solar masses. What I said was: "if we consider a 10 million solar mass black hole, the gravitational acceleration at the event horizon would be about one millionth that at the surface of a neutron star."

 Quote by Bernie G Because gravitational acceleration varies as the inverse of r squared.
Wait a minute - you are using Newton's law for this. I don't think you can use the weak-field approximation of the field equations at the event horizon of a black hole; IMO the full general relativistic treatment is needed.

 "Wait a minute - you are using Newton's law for this." Thats correct. I think the Tolman–Oppenheimer–Volkoff equation is baloney and that the pressure of a relativistic star inside a BH is simply given by the relativistic pressure of (rho)(c^2)/3. I am using gravitational acceleration varying as 1/(r^2) and don't define the pressure between the surface of the star and the event horizon. I specify a non-rotating star to avoid the relativistic velocities caused by conservation of angular momentum which Einstein believed would prevent collapse, and besides think (rho)(c^2)/3 would provide a supporting mechanism much larger than angular momentum. What formula for gravitational acceleration other than 1/(r^2) do you suggest? I'm open to it.

 Quote by Bernie G "Wait a minute - you are using Newton's law for this." Thats correct. I think the Tolman–Oppenheimer–Volkoff equation is baloney and that the pressure of a relativistic star inside a BH is simply given by the relativistic pressure of (rho)(c^2)/3. I am using gravitational acceleration varying as 1/(r^2) and don't define the pressure between the surface of the star and the event horizon. I specify a non-rotating star to avoid the relativistic velocities caused by conservation of angular momentum which Einstein believed would prevent collapse, and besides think (rho)(c^2)/3 would provide a supporting mechanism much larger than angular momentum. What formula for gravitational acceleration other than 1/(r^2) do you suggest? I'm open to it.
Well, for one thing there is no "relativistic star inside a BH"; beyond the event horizon there lies only the gravitational singularity, the exact form of which is as per yet unclear in the absence of a consistent theory of quantum gravity.
In the region of the event horizon itself relativistic effects are definitely significant, so to describe trajectories you will need to use one the solutions of the Einstein equations; since you are saying the black hole is static and has no charge, the Schwarzschild metric will probably be your metric of choice.
The TOV is not "baloney", but a direct consequence of above mentioned metric; saying that TOV is invalid amounts to saying that the Einstein equation, and hence GR, is wrong. That is a pretty strong statement, and will require equally strong evidence to support it.

Can I ask you please what it actually is you are trying to achieve ?

 I’m maintaining that its logical that a large relativistic star exists inside a BH, and its OK if we differ on this. It will be settled someday by the observation of the merger of two approximately equal mass black holes. If each contains a large relativistic star, a huge ejection of the upper layers of the stars will occur. Yes, in the region of the event horizon of a small black hole relativistic effects are significant. One would expect all the material in a collapsing star to go relativistic (quark matter + radiation). Most initial radiation would escape, and the remaining stuff would generate the almost unimaginable pressure of (rho)(c^2)/3. Saying that TOV is invalid does not amount to saying that GR is invalid. The event horizon of a trillion solar mass black hole has a gravitational acceleration about that at the surface of the earth, but TOV predicts infinite pressure there. That doesn’t make sense. I’m not analyzing charge or magnetic field effects of a black hole at this time, and think light cones are a good answer in the region between the event horion and the surface of the relativistic star. You didn’t answer... what formula for gravitational acceleration other than 1/(r^2) should be used?

 Quote by Bernie G I’m maintaining that its logical that a large relativistic star exists inside a BH, and its OK if we differ on this. It will be settled someday by the observation of the merger of two approximately equal mass black holes. If each contains a large relativistic star, a huge ejection of the upper layers of the stars will occur. Yes, in the region of the event horizon of a small black hole relativistic effects are significant. One would expect all the material in a collapsing star to go relativistic (quark matter + radiation). Most initial radiation would escape, and the remaining stuff would generate the almost unimaginable pressure of (rho)(c^2)/3. Saying that TOV is invalid does not amount to saying that GR is invalid. The event horizon of a trillion solar mass black hole has a gravitational acceleration about that at the surface of the earth, but TOV predicts infinite pressure there. That doesn’t make sense. I’m not analyzing charge or magnetic field effects of a black hole at this time, and think light cones are a good answer in the region between the event horion and the surface of the relativistic star. You didn’t answer... what formula for gravitational acceleration other than 1/(r^2) should be used?
Ok, I think you are mixing things up a little. The TOV equation is the relativistic form of the usual hydrostatic equations describing a hydrostatic system in equilibrium; it has a different form than the Newtonian version because of relativistic effects being taken into account. This equation doesn't have anything to do with Black Holes, them being the end product of a gravitational collapse.
As for acceleration at the event horizon, unfortunately there is no simple, straightforward formula one can use. Assuming the black hole is stationary and has no charge, you can calculate the Schwarzschild geodesics, which describe the trajectories of a small mass moving in the vicinity of the black hole, like so :

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

As you can see the maths involved in this are non-trivial, unlike in the Newtonian case.

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 Quote by Bernie G what formula for gravitational acceleration other than 1/(r^2) should be used?
You might find the following web page of use also-

7.3 Falling Into and Hovering Near A Black Hole

Generally, for a static black hole, the following equations is used when calculating the proper local acceleration of a black hole-

$$a_g=-\frac{Gm}{r^2}\frac{1}{\sqrt{1-2M/r}}$$

where M=Gm/c2

 3. GRAVITATIONAL TIME DILATION NEAR BLACK HOLE Gravitational time dilation is the effect of time passing at different rates in regions of different gravitational potential; the lower the gravitational potential (closer to the center of a massive object), the more slowly time passes. Albert Einstein originally predicted this effect in his theory of relativity and it has since been confirmed by tests of general relativity. Therefore the Black Hole can't be formed for an outer observer. In quantum gravity time is created by a number of quantum events. Each event results with a Planck's time dilation (lp) and therefore we perceive a flow of the time. Time doesn't exist as an independent fundamental property or phenomenon. We measure a distance and a time by a constant speed of light as a constant number of the quantum events which are passed by a photon N= R/lp. A distance and time become contracted by the number of Planck's units when there is an additional non-local information from a real massive particle with its Compton wave length ly= h/mc . We calculate the interference of the information from the direction of the observer and from the direction of the massive particle as a vector sum in a triangle. As we showed above N=M/m particles cause (M/m) [(lp /(ly/2) )] length contraction and proportional time dilation where ly is a Compton wave length information of the massive particle perpendicular to the information of the observer in vacuum. Therefore time (tf) is a sum : tf^2 (R/lp) = t0^2(R/lp) + tf^2 (M/m) [(lp /(ly/2) )] t0^2(R/lp) = tf^2 {(R/lp) - (M/m) [(lp /(ly/2) )]} where: lp * lp – Planck length squared = hG/c^3 Compton wave length ly=h/mc After substitution we receive a well known equation for gravitational time dilation: t0^2= (1-2GM/Rc^2 ) http://en.wikipedia.org/wiki/Gravita..._time_dilation
 Sorry for the long delay in responding. “you can calculate the Schwarzschild geodesics, which describe the trajectories of a small mass moving in the vicinity of the black hole” Thats where you’ve got it wrong. Does orbiting particle analysis descibe the general motion of a particle in a star or black hole? Are all the particles in our sun orbiting? Of course not. General kinetic energy equations can be used to describe a specific case like an orbitting particle, but you can not use a specific case like an orbiting particle to describe the general kinetic solution. For example, see: http://math.ucr.edu/home/baez/virial.html To use orbital particle dynamics to describe reality in a star is simply incorrect. Gas pressure or (rho)(c^2)/3 has no net velocity so relativistic equations are not needed. The TOV equation was not meant to apply to a BH, and it doesn’t even work that well for a neutron star. Saying that orbital particle dynamics is not the general support mechanism in a BH does not deny general relativity.
 In the Information Universe there aren't distances, motion, energy, time as the absolute values. The particle aren't orbiting. They do exchange the information from the space (vacuum) and the particle is moving toward the absorbed information. In the gravitational field there is a gradient of the density of the information toward the emiting particles of the massive body and we observe the oscillations and acceleration toward the massive body. The motion of a particle close to a star depends on the absorbed information and there are many different motions.