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

[Bernie G]

It doesn't change things much, but the gravitational potential energy of the proposed star is likely closer to (1.0)(GM^2)/R instead of my estimate of (0.82GM^2)/R.

 

[Bernie G]

"So you have in mind to identify a non-gravitational force that is able to resolve the singularity no matter how large the mass M of the object might be?"

Let me clarify. My estimates show (pc^2)/3 is more than sufficient to prevent core collapse up to 10 or 20 solar masses. Above that greater than (pc^2)/3 is needed. If you want I can show my estimates here for estimated core pressure due to gravity, and estimated core pressure generated by (pc^2)/3.

 

[Bernie G]

I might have made a mistake with the last statement. I never did core pressure estimates for larger black holes. If the star contained in a black hole is more or less a constant fraction of the Schwarzschild radius, then the star radius will be proportional to M. Since gravitational core pressure goes as (M^2)/(R^4), and if M is proportional to R, then larger black hole (neutron?) stars might have a smaller core pressure than that found in smaller black holes.

 

[Bernie G]

But I'd rather stick to discussing a star support mechanism inside smaller black holes. A star in a larger black hole could have a significantly different structure due to the weaker gravity in the outer layers of a large black hole.

 

[Bernie G]

Here are the pressure estimates of a hypothetical 3 solar mass star of 6 km radius with a relativistic core that generates pressure P = (pc^2)/3, where p is the density. Units used are kilogram/meter/seconds. These estimates show the core will not collapse even though the star radius is smaller than the Schwarzschild radius, ie.- the core pressure generated by (pc^2)/3 will exceed the core pressure due to gravitational compression. Please feel free to check these numbers and question the estimates:

(1) For the peak core pressure due to gravitational compression, which we can call CP, and assuming the star has a typical 1/r^2 density profile, CP should be given approximately as:

CP = (2GM^2)/(πR^4) = 1.3 X 10^36

(2) To calculate peak core density (and hence the generated pressure), assuming that half the star mass is contained within R/2, and assuming the peak density at the center is twice this average core density, the peak core density would equal 6 X 10^19. This is an astoundingly high number, more than 10 times the peak core density estimated in a neutron star, but that makes sense. With this peak core density, the pressure generated by (pc^2)/3 would equal 1.8 X 10^36, which is greater than CP (the pressure generated by gravitational compression).

 

[Bernie G]

Note that pi (3.14) shows up as typeface "π" in the above expression (2GM^2)/(πR^4).

 

[czes]

The Black Hole is an object with a maximum entropy for a given mass of the object.
Each particle is entangled with a number of non-local information on a longest distance = a circle of the object / Compton wavelength = [2 pi R / (h/mc)] in an object with a radius R and the whole mass M. How many bits of the information may contain M/m particles with an average mass "m" in a Black Hole where M=c^2 R /2G

(M/m) [2 pi R / (h/mc)] = pi R^2 / (hG/c^3 ) = A /4 lp^2

Where A is a surface of the Event Horizon of the Black Hole and lp^2 is Planck length squared.

It is interesting, that the information capacity of the Black Hole increases not with its volume but with its surface. Therefore the average density of the Black Hole Like Object decreases if the mass of the object increases.

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

 

[Phrak]

It would be very satisfying, if at some time in the not too distant future, discussions of black holes did not contain meaningless temporal verbage. The word "is" is the current tense of the verb "to be". "Will be" is the future tense the verb "to be", ect.

The use of such key words in general relativity, and even special relativity, should be specified with clarity or a declarative statement about black holes is so perfectly ambiguous it could mean a number of different things to diffenent readers.

If you wish to discuss back holes, you-all should be aware that the verbs "is", "was", "will be", "never was", "never will be", etcetera are not physically meaningful without greater specification nor universally understood within your own personal gestalt. spacetime is not flat.

 

[Bernie G]

"In the beginning there was nothing, which exploded." — Terry Pratchet

Why there should be something is a very tough question.

 

[mesinik]

"Why there should be something is a very tough question.

With saturday night logic (where time and space are curved a lot) it might be postulated: when space becomes gravitationally curved enough, then you will observe time like one of "normal" dimensions, while some "ordinary" dimension behaves somewhat similar to "normal" time.
So, could we turn the question back like that: why should something be there in the future and/or past?
(? Après nous la ...)

 

[Bernie G]

To sum up my position, there’s a lot of confusion out there about black holes, mostly caused by so many people repeating the illogical argument that black holes are a point singularity. They use the incorrect argument that anything within the event horizon (Schwarzschild radius) must have energy greater than mc^2 if it is not to proceed to the center. This is getting facts backwards. The maximum gravitational energy of a star is (0.6GM^2)/R. If ALL a star’s energy goes into creating pressure, that energy would equal Mc^2 maximum. Setting Mc^2 = (0.6GM^2)/R results in the minumum radius R for anything, or any star, including the star in a black hole, of R(min) = (0.6GM)/(c^2). This is 30% of the Schwarzschild radius. Any smaller radius would mean the gravitational energy would have to exceed Mc^2.

Actual stars in nature have density profiles of about 1/(r^2), resulting in a gravitational energy of almost exactly (1.0GM^2)/R, or simply (GM^2)/R. And if all (or almost all) the mass inside a black hole were to go “relativistic” (I hate using that term), the total energy creating pressure would be (Mc^2)/3. The viral theorem, which is used to calculate the size of gravitational objects, says the energy creating pressure equals half the gravitational energy, or (Mc^2)/3 = (GM^2)/2R. This gives the radius of a star inside a black hole of R = (1.5GM)/(c^2), which is 75% of the Schwarzschild radius. It doesn’t matter what this star in a black hole is made of, quark matter, radiation, whatever; that's the size. Other basic math shows that the core density and core pressure of a star in a small black hole (of a few solar masses) is about 8 times the core density and core pressure of a neutron star of a few solar masses. Nothing profound or unrealistic about this. Also, if the star inside a black hole has a “atmosphere” of radiation, it would be small and would not affect the above calculations. This hypothetical radiation wouldn’t come anywhere near the Schwarzschild radius and would be contained in much the same way the Earth contains its atmosphere.

An interesting result of the above is if two EQUAL mass orbitting black holes merge, there can be a huge ejection from them or even annihilation of the 2 black holes. Hmmm. Its only a matter of time before black hole mergers will be observed. Let's hope some observed mergers are of equal sized ones.

Finally, I don’t know why so many people use the Tolmann Volkov equation for a black hole. Not only does it give the wrong answer (neutron star collapse at 0.7 solar mass), but its conclusion of infinate pressure at the Schwarzschild radius is kind of obvious nonsense. But I do agree with Tolmann Volkov that the contents of a black hole can be analyzed as a gas, but one where the "gas" pressure P = (rho/3)c^2. Sorry for the length of this. If anyone has any questions on the above email Berniepie at aol.com.

 

[Bernie G]

Minor correction to the above: The core density of a resulting black hole is about 20 times the core density of a neutron star, and the core pressure of the black hole is about 50 times the core pressure of a neutron star (of a few solar masses). Shouldn't do calculations in my head. Doesn't change anything; if you can accept the densities and pressures in a neutron star, these densities/pressures are also imaginable. The biggest weird thing is that if a neutron star collapses to about 3/8 its size (in terms of radius), the resulting star is 25% smaller than the Schwarzschild radius and nothing can escape unless 2 equal size black holes merge.

 

[Bernie G]

Final tweaking: I think a thin neutron crust is unlikely since that would probably require a temperature gradient. Also, if the core is very large (a more likely density profile) the gravitational energy energy could be as low as (4GM^2)/(5R), resulting in a star radius of only (1.2GM)/(c^2) instead of R = (1.5GM)/(c^2). Bottom line is a non-rotating star of relativistic material would have a radius between 60 - 75% of the Schwarzschild radius, which with the bulging effect should be enough for a massive ejection to occur if two approximately equal size orbiting black holes merge.

This also presents a different possible “origin” of our universe other than the big bang. Consider if two massive orbiting black holes merged, with each approximately half the mass of the universe. They would eject relativistic material for millions of years.

 

[mesinik]

One possible bet is, there might be just an indetermined state (like future) because "normal" time is meshed up with other dimensions. It is fun to think about this at least.
If so, it's probably even more fun to build a ring around an extra large black hole (large enough, so the gravitation on the edge is affordable). Now, let's sit on this ring and push a mirror inside with a stick, beyond the event horizon ... OK, OK, let's just look at the Zeldovich-Starobinsky-Bekenstein-Hawking radiation. Could we see and hear the future and/or past? Anyway, this scenario looks and feels somewhat like an oracle from any mythology...

Both string theory and loop quantum gravity claim possible elimination of the black hole singularities. If that is true, what do they predict the inside of a stellar size black hole contains? Is it some new ultra dense state of matter, or something else?

I will try to ask various authorities this question at the APS meeting in St. Louis next week. But what’s your opinion? Has anything been published?

The only concrete proposal I am aware of is the Mathur fuzzball (hep-th/0502050).

Jim Graber

 

[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.

 

[Markus Hanke]

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.

Wrong.
How can the gravitational acceleration at an event horizon be smaller than at the surface of a neutron star ?

 

[Markus Hanke]

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.

 

[suprised]

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.

 

[mesinik]

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.

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.

 

[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.

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.

 

[Markus Hanke]

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.

 

[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 Schwarzschild 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.

 

[Markus Hanke]

“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 Schwarzschild 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...

 

[Bernie G]

"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."

 

[Markus Hanke]

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.

 

[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.

 

[Markus Hanke]

"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 ?

 

[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?

 

[Markus Hanke]

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.

 

[stevebd1]

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