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

Bernie G

If the radiation ball model described earlier is correct (0.75 Schwarzchild radius ), its possible for similar size merging black holes to partially or completely annihilate in a mini big bang.

Bernie G

I wonder if some of the merged galaxies that appear to have had an explosion in the center actually have had an explosion in the center. Its now accepted that when galaxies merge the super massive black holes in the center can also merge. If the radiation ball model is correct these super massive black hole mergers might result in a massive ejection.

Bernie G

Maybe a radiation star of R > 0.75 SR can exist in a black hole, as a partial radiation/quark mixture.

Bernie G

On the other hand, most internet sources say radiation pressure equals (1/3)pc^2 and that gravitational potential energy for a neutron star (or radiation star) should equal (GM^2)/R. Using the viral theorem then also gives R = 0.75 SR for a radiation star. I'll try to get some authoritative opinion on this within a week.

stevebd1

The other thing to consider is that inside 2M, r is temporal (as t is temporal outside 2M) so you would also have to consider the spacetime metric which would have to switch from space-like to time-like again in order to maintain a stable radius, is there a solution/form synonymous with Schwarzschild metric that suits this and incorporates a radiation star? The switch back to time-like space does occur with a charged and/or rotating black hole, though the charged solution is considered not very realistic as the universe has a tendency to neutralise any object with a charge. In its own way, the Schwarzschild solution is also deemed unrealistic due to the fact that it is an absolutely static solution whereas it's almost certain that no matter how small, all celestial objects have some degree of spin. The event horizons for black hole with spin are-

[tex]r_\pm=M\pm\sqrt{M-a}[/tex]

where [itex]r_\pm[/itex] represents the outer and inner horizon, spacetime becoming space-like in the radial at r₊ and reversing to time-like at r_-. The boundary of the radiation star (ring even) might occur within or at the inner horizon though the inner horizon (or Cauchy horizon) is sometimes described as the boundary of predictability, itself being a contender for a weak singularity.

Bernie G

To continue, to calculate the radius of a non-spinning, non-magnetic star in a black hole using the viral theorem, here’s the best formulas I’ve found so far for radiation pressure and gravitational potential energy of a gas star of density profile 1/r^2. If anybody can suggest better formulas, please do!

Most sources state the pressure exerted by radiation is one third of its average energy density. That sounds sensible. Even relativists would probably agree that as material collapses into a black hole, all or much of it becomes relativistic no matter what form it takes (radiation, neutrons, or exotic matter), and the maximum pressure it would exert should be one third of its average energy density if all the matter was converted into relativistic particles or radiation. Therefore (1/3)Mc^2 should be the maximum support energy of any form of star, and this should determine the minimum radius. (The radius would be larger if not all the mass was converted to relativistic form.)

Most sources say the gravitational potential energy of a gas star of density profile 1/r^2 is about (GM^2)/R , but I’m not satisfied with that formula and have estimated that the gravitational potential energy is 28% higher than that of a constant density profile star [ (0.6GM^2)/R ], or about (0.82GM^2)/R. If anybody wants to know how this estimate was done, or has a better estimate, please speak up.

Using the viral theorem, if (1/3)Mc^2 = (0.41GM^2)/R , then R = 1.23GM/c^2. This means, if you use this train of thought, that the minimum radius of a star inside a black hole should be at least 61.5% of the Schwarzchild radius. This very possibly is not large enough for a huge ejection to occur if 2 equal size small black holes merge. But again, the star should be larger than 61.5% of the SR if not all the mass is in relativistic form, which is very possible and probably likely. Hopfully the merger of 2 objects identified as nearly equal mass black holes will be observed in the next few decades. That’s about the best I can do at this time. If anybody has any suggestions or comments, fire away.

BTW, here’s an interesting tidbit, for what its worth. So far, of the 2000 observed neutron stars the largest have a mass of 1.97 solar mass, and this is probably near the upper limit. Also, of the 20 observed small black holes in the Milky Way, so far the smallest equals about 5 solar mass.

pari777

We recently had a lecture on black holes in the college. We were told about the new development going on in the field of theoretical physics on black holes. The prof. was telling that most of the singularities have been removed 2 a great extent but introducing another different set of co-ordinate system.

tom.stoer

Exactly, most of the singularities; this thread is about the singularity that cannot be removed by a clever joice of coordinates.

If you look at the Schwarzschild metric

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

you find that it's singular at r=0 and r=2M. The latter singularity is due to the choice of the coordinates and can be removed, e.g. via Eddington-Finkelstein- and Kruskal-Szekeres- coordinates:

http://en.wikipedia.org/wiki/Schwarz...nd_black_holes

The singularity at r=0 is not due to coordinates but is 'real'. This can be seen by looking at coordinate-independent scalars, e.g. the Kretschmann invariant

http://en.wikipedia.org/wiki/Curvatu...ral_relativity)

which is obtained from a special contraction of the Riemann curvature tensor. The Kretschmann invariant scales as K(r) ~ 1/r⁶. Now you could use a different coordinate system; the function for K expressed in the new coordinates would look different, but at the space time point which corresponds to r=0 the Kretschmann invariant will again be singular.

allintuition

I've enjoyed this thread, but I have been missing some mention of the experimental record. No naked singularities have ever been detected so the black hole as a singularity is in the same company as monopoles and decaying protrons. If no singularities are produced at the LHC it might be time to give them up altogether.

There is recent data supporting a subsequent stage to a neutron star where matter flows without viscosity (http://www.nasa.gov/mission_pages/ch.../casa2011.html). This view receives interesting support from attempts to create a quark-gluon plasma (www.bnl.gov/rhic) which finds that at enormous temperatures protons appear to "melt" into a non-viscous state. The simple, classical way to explain what is happening is that when matter is sufficiently compressed a force arises that is powerful enough to resist gravity. We know that such short range powerful forces exist because the weak force behaves in this way.

Does anyone following this thread know of any attempts to explain why such quasi-superfluid states exist at enormous pressures and temperatures? Based on the present evidence, it seems possible that black holes may be superfluids.

tom.stoer

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?

The first problem is that afaik no such force is known.

The second problem is that in order to understand GR (and QG) the singularity has to be resolved by gravity itself. You cannot expect that a theory X saves a theory Y that fails at a singuarity. It's up to Y (or an extension of Y) to cure itself.

allintuition

You have answered my question as to whether or not you know of someone who is trying to explain the non-viscous states of matter seen recently at BNL and by NASA trying to explain the behavior of a spinning high mass neutron star. The answer appears to be no. I hope I can provide something of an answer to your questions.

Thinking classically, although I know that this may be inappropriate, I see that with helium superfluids, both He-4 (bosonic) and He-3 (fermionic) repel themselves after London forces are switched off due to extreme cooling. This possible repulsive force is of the same magnitude as that of gravity. If we imagine that it is an inverse square law force, compressing matter, whether in a neutron star or at the RHIC, would be able to reproduce the non-viscous behavior that we see with helium superfluids. The search for a fifth force that opposes gravity with roughly the same magnitude is ongoing with no clear result so far (http://en.wikipedia.org/wiki/Fifth_force). I don't know of any attempt to incorporate such a fifth force into our understanding of GR at this time. So the answer to your first question is that there are some who would very much like to see a fifth force, but results thus far are inconclusive due to the weakness that such a fifth force is expected to have at normal pressures and densities.

The second question has to do with theories, but I would like to consider only GR. The discovery of dark energy, though no such potential force had been identified during Einstein's life, did not upset GR because its behavior was consistent with the cosmological constant term. GR is well-defined only up to the Schwarzschild radius. A force which prevented a singularity (not the singularity at 2M which depends on the coordinate system which you have pointed out, but the singularity at 0) would not necessarily do any harm to GR just as dark energy has done no harm to GR. The question would be whether or not such a force would have an effect at lower matter densities where we do depend on GR, outside the Schwarzschild radius. Extremely careful measurements at the University of Washington (http://www.npl.washington.edu/eotwash/) so far indicate no additional forces at normal temperatures and densities.

I am suggesting the existence of a fifth force (sixth if we count dark energy). The possibility of a fifth force is not new. If I am suggesting anything new, it is that this fifth force will only be seen at extreme density or at very low temperature. Thanks for your response, by the way. I enjoyed thinking about the questions that you posed.

Bernie G

I think allintuition is on the right track by bringing up a quark-gluon plasma or other force in the core. One thing we can safely conclude about the core is that it is not neutrons. I no longer believe a star in a black hole would be a radiation ball. With a distributed mass star in a black hole (instead of a singularity), if all the matter was relativistic, pressure would be (pc^2)/3, and this pressure is so great it would force the mass far out beyond the Schwarzchild radius. A quark-gluon plasma in the core makes sense, and quarks have a higher collapse pressure than neutrons. But as for the upper layers and surface of the star, I think that could be neutrons since the pressure there is similar to pressures found in a neutron star.

tom.stoer

Even the QGP would not resist the collaps b/c it's not a specific interaction but simply the Fermi degeneration pressure that acts as a repulsive force. This is not sufficient to keep a massive neutron star stable and it would not change that much for a QGP- or a quark-star

Have a look at http://en.wikipedia.org/wiki/Degener...ark_degeneracy

Bernie G

But (pc^2)/3 is more than sufficient to prevent collapse.

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?"

Yes. For one model I think something roughly similar to a conventional neutron star could exist within the Schwarzchild radius. The upper layers and surface of the star could be neutrons since the pressure there is similar to pressures found in neutron stars. But pressures and densities in the core would be so great that the core material would go "relativistic" and generate a pressure of (pc^2)/3. It doesn't matter what the core is made of (quarks, etc), so long as it generates (pc^2)/3. The star might even have a radiation "atmosphere" - all located well within the Schwarzchild radius. But my earlier estimate of star size would be a little off because the upper layers would be supported mostly by neutron degeneracy pressure, which would be smaller than (pc^2)/3.

tom.stoer

what would be the equation of state?

afaik for a neutron star one uses p = ρ/3 which is ultra-relativistic and which does not prevent a collaps.

Bernie G

All thats needed is to prevent core collapse, since that's where collapse happens. I don't think P = (pc^2)/3 is used for a neutron star core prior to collapse. But I think it would apply after core collapse.