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). Best, Jim Graber
http://arxiv.org/abs/0712.0817 "We show that the singularity is replaced by a bounce at which quantum effects are important and that the extent of the region at the bounce where one departs from classical general relativity depends on the initial data." Might be helpful to you.
Good suggestion Shalayka! http://arxiv.org/abs/0712.0817 is a recent paper of Gambini Pullin and Campiglia. Jim Graber, you ask "Has anything been published?" Plenty has been published in that general direction. here are some references. This is far from complete. I am excluding papers that deal only with the horizon or the exterior. This is a sample of loop papers having to do with the black hole interior. A fair number of these papers were published in Physical Review Letters or in Physical Review D. http://www.slac.stanford.edu/spires...D+DATE+>2004&FORMAT=www&SEQUENCE=citecount(d) 1) Quantum geometry and the Schwarzschild singularity. Abhay Ashtekar (Penn State U. & Potsdam, Max Planck Inst.) , Martin Bojowald (Potsdam, Max Planck Inst. & Penn State U.) . IGPG-05-09-01, AEI-2005-132, Sep 2005. 31pp. Published in Class.Quant.Grav.23:391-411,2006. e-Print: gr-qc/0509075 References | LaTeX(US) | LaTeX(EU) | Harvmac | BibTeX | Keywords | Cited 48 times 2) Black hole evaporation: A Paradigm. Abhay Ashtekar (Penn State U.) , Martin Bojowald (Potsdam, Max Planck Inst. & Penn State U.) . IGPG04-8-4, AEI-2004-072, Apr 2005. 18pp. Published in Class.Quant.Grav.22:3349-3362,2005. e-Print: gr-qc/0504029 References | LaTeX(US) | LaTeX(EU) | Harvmac | BibTeX | Keywords | Cited 39 times 3) A Black hole mass threshold from non-singular quantum gravitational collapse. Martin Bojowald (Potsdam, Max Planck Inst.) , Rituparno Goswami (Tata Inst.) , Roy Maartens (Portsmouth U., ICG) , Parampreet Singh (Penn State U.) . AEI-2005-020, IGPG-05-3-3, Mar 2005. 4pp. Published in Phys.Rev.Lett.95:091302,2005. e-Print: gr-qc/0503041 References | LaTeX(US) | LaTeX(EU) | Harvmac | BibTeX | Keywords | Cited 34 times 4) Nonsingular black holes and degrees of freedom in quantum gravity. Martin Bojowald (Potsdam, Max Planck Inst.) . AEI-2005-115, Jun 2005. 4pp. Published in Phys.Rev.Lett.95:061301,2005. e-Print: gr-qc/0506128 References | LaTeX(US) | LaTeX(EU) | Harvmac | BibTeX | Keywords | Cited 27 times 5) Spherically symmetric quantum geometry: Hamiltonian constraint. Martin Bojowald, Rafal Swiderski (Potsdam, Max Planck Inst.) . AEI-2005-171, NI05065, Nov 2005. 33pp. Published in Class.Quant.Grav.23:2129-2154,2006. e-Print: gr-qc/0511108 References | LaTeX(US) | LaTeX(EU) | Harvmac | BibTeX | Keywords | Cited 19 times Some more here: FIND DK LOOP SPACE AND DK BLACK HOLE AND DATE >2005 6) Wave functions for the Schwarschild black hole interior. Daniel Cartin (Naval Acad. Prep. School, Newport) , Gaurav Khanna (Massachusetts U., North Dartmouth) . Feb 2006. 14pp. Published in Phys.Rev.D73:104009,2006. e-Print: gr-qc/0602025 References | LaTeX(US) | LaTeX(EU) | Harvmac | BibTeX | Keywords | Cited 5 times 9) Loop Quantum Dynamics of the Schwarzschild Interior. Christian G. Boehmer (University Coll. London & Portsmouth U., ICG) , Kevin Vandersloot (Portsmouth U., ICG & Penn State U.) . Sep 2007. 15pp. Published in Phys.Rev.D76:104030,2007. e-Print: arXiv:0709.2129 [gr-qc] References | LaTeX(US) | LaTeX(EU) | Harvmac | BibTeX | Keywords | Cited 5 times 10) Gravitational collapse in loop quantum gravity. Leonardo Modesto (Bologna U. & INFN, Bologna) . Oct 2006. 16pp. Published in Int.J.Theor.Phys.47:357-373,2008. e-Print: gr-qc/0610074 References | LaTeX(US) | LaTeX(EU) | Harvmac | BibTeX | Keywords | Cited 4 times
shalayka and Marcus, Thank you for the very good references. I have printed them out and am starting to study them. At first glance, the answer to my question which most of these papers seem to be promoting is a very dense Planck scale "spacetime foam" or "quantum geometry breakdown of spacetime" surrounded by a Kantowski-Sachs vacuum solution. Do you agree? Thanks again. Jim Graber
Heavens! I don't know as I would recommend anyone to read these articles. Except what Shalayka said, maybe. The Gambini Pullin Campiglia one is recent and IIRC comparatively brief and clear. Jim I admire your energy and curiosity and I am very glad you plan to ask the appropriate people at the APS meeting. Jim you asked was anything published about this? I listed that stuff just to show concretely a sample of what had been published. But I don't BELIEVE we humans have any very good notion of what happens down a black hole and all this work must necessarily be preliminary. The people doing it, if they are good, probably realize this better than anyone else. What I believe is that geometry and matter are fundamentally the same and arise from the same basic microscopic D.O.F. stuff. When it is very compressed, the distinction between matter and space disappears and one gets down to a stew of microscopic degrees of freedom, which we don't yet know how to model mathematically. I believe it is the same kind of stuff that was there at bigbang time, at the beginning of expansion. That is, the stuff precedes classical cosmology. And the reason people call it FOAM is because by Heisenberg the geometry would have been very chaotic and unsmooth and hard to pin down. The endpoint of something more and more complicated is something perfectly simple---call it foam, or Planck goo, or the Fire of Heracleitus. Or don't call it anything because we don't yet have a credible mathematical model so there is no convincing metaphor. It isn't "like" anything, yet. that's just my attitude for the time being. ======================== Heracleitus born c. 540 BC, Ephesus, in Anatolia [now Selçuk, Tur.] died c. 480 Greek philosopher remembered for his cosmology, in which fire forms the basic material principle of an orderly universe. Little is known about his life, and the one book he apparently wrote is lost. His views survive in the short fragments quoted and attributed to him by later authors...
Hi jim--- Marcus is a bit biased towards one way of thinking (as I am, admittedly). You may find more interesting the following paper about the ``fuzzball'' paradigm proposed by Samir Mathur. http://arxiv.org/abs/0804.0552 The picture solves many of the problems with traditional black hole physics, some of which are generically present in other approaches to quantum gravity.
One other point of view given recently is that of Christoph Schiller (the person responsible for the free physics textbook "Motion Mountain"). http://www.motionmountain.net/research/research.html In the second paper of his series of four ("General relativity, gravitons and cosmology deduced from extended entities") he goes on to describe a method which logically removes black hole and universal (big bang) singularities. Opinion may vary, and as far as I know, this work is not peer-reviewed yet. Even then, I found that it may be helpful to describe the thought patterns behind attempts at quantizing spacetime, and is also a good review of the more important tried-and-"true" equations related to General Relativity. From what I can gather, Schiller's method may classify as a fuzzball. P.S. I am naturally biased towards fuzzball methods mostly because I really love cats and they are generally cute little fuzzballs as well. Except for those hairless ones -- they're more like a naked singularity, I guess. :)
Quantum gravity singularity elimination talks. I did hear Abhay’s and Gary’s talks yesterday. Basically, nothing was said that has not previously been published. Both agreed that singularities are probably eliminated by quantum gravity. Abhay talked mostly about cosmology, but said during the question period that similar things applied to black holes but the work was not as advanced and that the picture on the post collapse side still needed details worked out. But he said he was sure there was no singularity. Gary also said recent work favored no singularities, but he said he only had two strong arguments, not a proof. One argument, primarily due to Eva Siverstein, was perturbative and based on tachyon condensation smoothly pinching off the space before the singularity was reached. The other nonperturbative argument was based on Maldacena duality and concluded that a black hole could not exist because an infinite redshift event horizon could not exist without contradicting the Maldacena dual description. During the comment period Abhay said he doubted the second argument because it was too dependent on analyticity. He went on to say however that he also thought there was no event horizon, only an isolated horizon or a dynamic horizon. I had read or heard this before, but I thought this was only a mathematical technicality. However, Abhay seemed to think it was a necessary part of singularity elimination. I’ll probably post more later about the size of the “Planck goo”. The key phrase is “Planck density”, not “Planck length.” Bye for now. Best, Jim Graber
I think the question basically is: Can intense radiation pressure be the support mechanism inside a black hole? I think it is logical that when a star above several solar masses collapses, the neutrons in the core disintegrate into radiation and some quark matter. As the collapse continues and temperature rises still further virtually all matter converts to radiation. If the radiation is contained in the system, the pressure of the radiation should be P = pc*2 , where p is the equivalent mass density of the radiation. The contained radiation, which has mass, basically acts like a compressed gas that can generate pressures exceeding neutron collapse pressure. As I understand the TOV equation, dP/dr is proportional to p + P, which means if P is high enough there is runaway collapse. I don't think Einstein accepted this equation because he didn't believe in a point singularity.
According to LQG the interior of a black hole horizon is nothing else but a huge intertwiner, which means ordinary space.
That reminds me of a paper by Krasnov and Rovelli where they concluded that "for an observer at infinity" the black hole was described somewhat in that way. The Hilbert space of BH states was the space of intertwiners of some size determined by the area of the horizon. So a BH state (for an observer at infinity) would be an intertwiner. But maybe there isn't yet one clear answer in the LQG context. I did a spires search on keywords "black hole and quantum gravity, loop space" and came up, for instance, with this: http://arXiv.org/abs/0805.1187 Black holes in loop quantum gravity: the complete space-time Rodolfo Gambini, Jorge Pullin 4 pages, 2 figures (Submitted on 8 May 2008) "We consider the quantization of the complete extension of the Schwarzschild space-time using spherically symmetric loop quantum gravity. We find an exact solution corresponding to the semi-classical theory. The singularity is eliminated but the space-time still contains a horizon. Although the solution is known partially numerically and therefore a proper global analysis is not possible, a global structure akin to a singularity-free Reissner--Nordström space-time including a Cauchy horizon is suggested." The Krasnov Rovelli paper gives a different picture (specialized as it is from a particular observer's point of view): http://arXiv.org/abs/0905.4916 Black holes in full quantum gravity Kirill Krasnov, Carlo Rovelli 5 pages (Submitted on 29 May 2009) "Quantum black holes have been studied extensively in quantum gravity and string theory, using various semiclassical or background dependent approaches. We explore the possibility of studying black holes in the full non-perturbative quantum theory, without recurring to semiclassical considerations, and in the context of loop quantum gravity. We propose a definition of a quantum black hole as the collection of the quantum degrees of freedom that do not influence observables at infinity. From this definition, it follows that for an observer at infinity a black hole is described by an SU(2) intertwining operator. The dimension of the Hilbert space of such intertwiners grows exponentially with the horizon area. These considerations shed some light on the physical nature of the microstates contributing to the black hole entropy. In particular, it can be seen that the microstates being counted for the entropy have the interpretation of describing different horizon shapes. The space of black hole microstates described here is related to the one arrived at recently by Engle, Noui and Perez, and sometime ago by Smolin, but obtained here directly within the full quantum theory." The spires search, if anyone wants to see all the LQG black hole papers with date > 2004: http://www.slac.stanford.edu/spires...D+DATE+>2004&FORMAT=www&SEQUENCE=citecount(d) Spires finds 76 papers
Tom, I decided there was too much old stuff in that search, given how much the field has changed in the past 3 years. So instead of setting the date at 2004, I changed to 2007: http://www.slac.stanford.edu/spires...D+DATE+>2007&FORMAT=www&SEQUENCE=citecount(d) Now it gives 45 papers and all have the date > 2007. It may surprise readers to see which papers are the most-cited. The more highly cited ones are listed first.
I am actively working on this fuzzball thing. We are able to find what we call "bubbling solutions" for very special kinds of 5-dimensional black holes. These are solutions that from infinity look like a black hole, but the geometry is regular everywhere and there are no horizons. Instead of a singularity, the solutions have a deep throat with pieces of nontrivial topology at the bottom, which we call "bubbles". There are no pointy bits (singularities), but only smooth bits of 2-homology. The idea is that these solutions represent microstates, and the horizon of a physical black hole arises as an emergent phenomenon when you consider the statistical fluctuations of the geometry at the bottom of the throat. Here is the canonical review paper, if you're interested: http://arxiv.org/abs/hep-th/0701216 Right now we're working on finding bubbling solutions for slightly less special kinds of black holes...however, this is quite a bit more difficult, as the equations get rather nasty.
Motl had an interesting blog article about this, a while back, in relation to whether AdS/CFT can say anything interesting, he concluded "At the center of black holes, something bad is happening to time which is much more drastic an event than when space shrinks...."
There are at least a couple of papers where (in a particular model inspired by LQG) to find the answer : 1) arXiv:0905.3170 Self-dual Black Holes in LQG: Theory and Phenomenology Leonardo Modesto, Isabeau Prémont-Schwarz Journal-ref: Phys.Rev.D80:064041,2009; 2) arXiv:0811.2196 Space-Time Structure of Loop Quantum Black Hole Leonardo Modesto Int.J.Theor.Phys.49:1649-1683,2010.
I'm not thrilled with the theories about what's inside a black hole. A point singularity seems to be one of the worst explanations; where there is a lack of understanding a poor simplification is given as logical.
just an idea, but what if a blackhole is created by the universe moving outward like currents create whirlpools and that the singularity is not there at all.but instead it is spat back out the otherside to create a new energised matter. I also read a theory about the big bang starting from a singularity if that were the case wouldn't the universe be going the complete other direction, being drawn into, not being pushed away.just thinking.
That sounds too weird. I think simply a radiation ball exists inside the Schwarzchild Radius, with a density profile similar to that of a conventional star (denser closer to the core). I think this because neutrons can not exist at these high pressures and energies. Radiation pressure would be the supporting mechanism. This might be confirmed by observation within 20 years by observing the merger of 2 typical 8 solar mass black holes in other galaxies. (Roughly perhaps 100 mergers of neutron stars and black holes occur annually, so about one black hole - black hole merger should occur annually.) If the radiation ball size is ≥ 70% of the Schwarzchild radius, a large observable burst of radiation will occur, but if the black holes are a point singularity nothing will be ejected of course. I hope to have a good estimate soon for the size of this theoretical radiation ball, but have to get a formula for the radiation pressure P first. P should be equal to (1/3)pc^2 or (2/3)pc^2 or pc^2, where p is the radiation density.
There are several proposals from ceratin theories of quantum gravity, i.e. the fuzzball proposal in string theory and a 'huge intertwiner' in loop quantum gravity. In both cases the singularity is resolved by quantum effects.