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Quantum evaporation of a naked singularity

  1. Jul 1, 2005 #1

    marcus

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    this seems to be an interesting paper,
    though I can't tell for sure (don't understand the idea of naked singularity well enough, how you can have one)

    http://arxiv.org/abs/gr-qc/0506129
    Quantum evaporation of a naked singularity
    Rituparno Goswami, Pankaj S. Joshi, Parampreet Singh
    4 pages, 2 figures

    "We investigate here gravitational collapse of a scalar field model which classically leads to a naked singularity. We show that non-perturbative semi-classical modifications near the singularity, based on loop quantum gravity, give rise to a strong outward flux of energy. This leads to the dissolution of the collapsing cloud before a naked singularity can form. Quantum gravitational effects can thus censor naked singularities by avoiding their formation. Further, quantum gravity induced mass flux has a distinct feature which can lead to a novel observable signature in astrophysical bursts."

    I've been looking up earlier Pankaj Joshi papers. I believe he is considered expert on the end states of gravitational collapse and on naked singularities. I don't understand about naked singularities. Apparently if the collapsing matter starts out distributed right you can have collapse without an event horizon forming.

    If anyone has some intuition they want to share, please do.

    In Loop Quantum Cosmology an inhomogeneous model (spherically symmetric) is being worked out. able to deal with this. an earlier LQC result was that inflation is generic in a BB. you dont have to explain it by postulating something extra, you get it out of the basic LQC model.
    something like that seems to be happening here.
    Goswami, Joshi, Singh talk about a "negative pressure" quantum effect which blows apart the singularity that is trying to form

    so there is a burst of energy and you NEVER GET a naked singularity.

    it sounds to me like they are talking about something like a GRB gammaray burst mechanism

    Of course LQG and the applied version symmetry-reduced LQC could both be wrong---but we dont know that they are wrong and they keep going ahead and getting interesting results. Assuming it is not wrong, this result is very curious.

    Maybe we should give these three authors a handle like GJS or G-J-S and keep tabs on this paper. and earlier papers by Joshi about naked sings and collapse endstates and stuff. the earlier papers might actually explain more because they are earlier and you can easily get them listed by the arxiv search engine.
     
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  3. Jul 1, 2005 #2

    Chronos

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    Indeed, I had the same impression marcus - a potential GRB mechanism. I think the authors are being properly cautious until they have some hard numbers that are consistent with observational evidence before taking it to the next level. And I'm all in favor of ridding the observable universe of naked singularities. I can't accept that a singularity would be so disrespectful of its clothed brethren as to cavort about in public where anyone could just look and see what really is inside the event horizon.

    Singh has written a number of interesting papers on singularities. He is also very active in LQG, which appears to have inspired his interest in singularities. This particular paper is an extension of his last paper, which is also quite interesting:

    http://arxiv.org/abs/gr-qc/0503041
    Title: A black hole mass threshold from non-singular quantum gravitational collapse
    Authors: Martin Bojowald, Rituparno Goswami, Roy Maartens, Parampreet Singh
     
  4. Jul 1, 2005 #3

    marcus

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    yes, what utter shamelessness! :smile:

    if this goes on he will become known as P. "singularity" Singh.

    yes there seems to be a cluster of papers about Black Hole coming out by Bojowald and his associates.

    ==========================
    George, thanks for your reply IN THE NEXT POST!
    I will respond here by editing a link or two into mine after reading yours.
    http://scienceworld.wolfram.com/physics/NakedSingularity.html
    It looks like I need to find something by Cristodoulou, from 1994 or 1999.
    It may be exactly as you indicate, that it depends on having electrically charged matter so that electrostatic repulsion in some sense overcomes gravitational attraction. or a huge amnt of angular momentum
    http://arxiv.org/abs/math.AP/9901147
    "One of the fundamental unanswered questions in the general theory of relativity is whether "naked'' singularities, that is singular events which are visible from infinity, may form with positive probability in the process of gravitational collapse. The conjecture that the answer to this question is in the negative has been called "cosmic censorship.'' The present paper, which is a continuation previous work, addresses this question in the context of the spherical gravitational collapse of a scalar field."
    AAARGH I am still not getting anything understandable. Here is
    http://arxiv.org/abs/gr-qc/9807019, a speculative article apparently. can naked sings make GRBs?
    here is a Joshi paper http://arxiv.org/abs/gr-qc/9806055
    here is a TP Singh easyreading review http://arxiv.org/abs/gr-qc/9806055
    "Gravitational Collapse, Black Holes and Naked Singularities
    T. P. Singh
    17 pages,
    This article gives an elementary review of gravitational collapse and the cosmic censorship hypothesis. Known models of collapse resulting in the formation of black holes and naked singularities are summarized. These models, when taken together, suggest that the censorship hypothesis may not hold in classical general relativity. The nature of the quantum processes that take place near a naked singularity, and their possible implication for observations, is briefly discussed."

    here is a possibly interesting TP Singh article
    http://arxiv.org/abs/gr-qc/9805062
    "Gamma-Ray Bursts and Quantum Cosmic Censorship
    T. P. Singh (Tata Institute, Mumbai)
    6 pages. This essay received the third award from the Gravity Research Foundation for the year 1998
    Gen.Rel.Grav. 30 (1998) 1563-1567
    Gamma-ray bursts are believed to result from the coalescence of binary neutron stars. However, the standard proposals for conversion of the gravitational energy to thermal energy have difficulties. We show that if the merger of the two neutron stars results in a naked singularity, instead of a black hole, the ensuing quantum particle creation can provide the requisite thermal energy in a straightforward way. The back-reaction of the created particles can avoid the formation of the naked singularity predicted by the classical theory. Hence cosmic censorship holds in the quantum theory, even if it were to be violated in classical general relativity."

    that is probably enough to go on for now
    oh, one more link,
    http://arxiv.org/gr-qc/0504019
    "A resolution of spacetime singularity and black hole paradoxes through avoidance of trapped surface formation in Einstein gravity
    Rituparno Goswami, Pankaj S. Joshi
    7 pages, 1 figure
    The occurrence of a spacetime singularity indicates the breakdown of Einstein gravitation theory in these extreme regimes. We consider here the singularity issue and various black hole paradoxes at classical and quantum levels. It is pointed out that a possible resolution to these problems could be arrived at by avoiding the formation of trapped surfaces during a continual gravitational collapse. A class of perfect fluid collapse models is constructed which realizes such a possibility. While the pressure could be negative in the interior of the cloud, the weak energy condition is satisfied. The collapsing star radiates away most of its matter as the process of gravitational collapse evolves, so as to avoid the formation of trapped surfaces and the spacetime singularity. The collapsing interior is matched to an exterior which is a generalized Vaidya spacetime to complete the model."
    =========================
     
    Last edited: Jul 2, 2005
  5. Jul 2, 2005 #4

    George Jones

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    I don't know much about this, but the spacetimes of charged Reissner-Nordstrom and rotating Kerr black holes can both contain naked singularities if there is enough charge and angular momentum respectively. These situations are very unphysical, though.

    On a Penrose diagram, the singularity or a charged black hole is vertical, i.e., timelike. When Q < M, there are 2 horizons. As Q approaches M, the horizons move closer together, when Q = M, they merge into one horizon, and when Q > M, there is no event horizon! So, for Q > M, there is a timelike singularity, accessible, in principle, to everyone!

    Joshi wrote a book, Global Aspects in Gravitation and Cosmology, in which there is lots of interesting stuff on physics and cosmology, but which probably now is a bit dated.

    Regards,
    George
     
  6. Jul 2, 2005 #5

    marcus

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    George your response here has been enormously helpful to me by getting me to struggle some with the literature and also to pay attention to Joshi.
    Here are his 41 papers going back to 1992.
    http://arxiv.org/find/grp_physics,grp_math/1/au:+Joshi_P/0/1/0/all/0/1
    He seems always to have been at Tata Inst.

    I see from your link that Oxford U.P. first published his book in 1994 and then in 1997.

    The wild card in the deck here is that in LQC (the cosmology reduction of LQG) inflation occurs naturally at very high density/curvature without having to invent an "inflaton". So you get the effect of a negative pressure scalar field generically or naturally from the time evolution difference equation.

    Now earlier this year Joshi wrote this paper which constructs a collapse to naked singularity using a negative pressure matter field. This was a CLASSICAL Gen Rel paper that just had an unusual matter equation of state which Joshi said was all right because look at "dark energy" and "inflatons" and "quintessence"---if everybody else is going to allow negative pressure then why not consider it. He got that the collapsing star might totally blow off all its energy to infinity and an event horizon never form! The star could collapse and evaporate at the same time and end up as nothing---with something like a GRB fleeing to infinity.

    http://arxiv.org/gr-qc/0504019
    "A resolution of spacetime singularity and black hole paradoxes through avoidance of trapped surface formation in Einstein gravity
    Rituparno Goswami, Pankaj S. Joshi
    7 pages, 1 figure

    So now the stage was set to put the two things together. LQG would supply the negative pressure regime at the heart of the collapse, and Joshi would supply the model where the star completely evaporates and doesnt leave anything.

    he even has it smoothly and seamlessly leave nothing but flat Minkowski space behind----totally weird.

    So Joshi just needed to write this paper, that this thread is about, and cite papers by Bojowald and any of various coworkers (Roy Maartens, Parampreet Singh, Tsujikawa, Ganashyam Date....) about how inflation was automatic in Loop Quantum Cosmology.

    of course I am woefully oversimplifying the story, just trying to connect the dots in a crude overall way.
     
    Last edited: Jul 2, 2005
  7. Jul 2, 2005 #6

    wolram

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    This is a crock, i was told in a highly respected forum that naked singularities
    can not exist.
     
  8. Jul 2, 2005 #7

    marcus

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    wolram you are too much! :biggrin:
     
  9. Jul 2, 2005 #8

    George Jones

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    Many years ago, Roger Penrose hypothesized that Mother Nature is a prude and does not allow her singularities to run around without clothes, i.e., event horizons. Almost, 15 years, Shapiro and Teukolsky said that while using a powerful computer, they caught a glimpse of some spindly string-bean naked singularities that could go high in the draft of Thorne's Hoops program. Wald has claimed that the singularities glimpsed by Shapiro and Teukolsky are of the computer generated virtual reality types and are not live, flesh and blood real singularities.

    So the status of Cosmic Censorship is still very much up in the air. Even if Mother Nature does employ a cosmic censor, it's not clear whether the censor is weak-willed or strong-willed.

    Regards,
    George
     
  10. Jul 2, 2005 #9

    marcus

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    Wolram, Joshi's work is not a crock.
    Read post #1 of thread
    In classical Gen Rel, naked sings can exist.
    Wolram you were misinformed by your highly respected source.
    Because Gen Rel allows naked sings, people like hawking have invented an extra postulate called "cosmic censorship" which ASSUMES without proof that they do not exist.

    that is a very unsatisfactory state of affairs----I tell you that in my model nakeds can't exist because, by hand, I put a special axiom in my model which says (surprise!) that they can't exist.

    Now Joshi comes on the scene and says to use QUANTIZED Gen Rel, some version of LQG, or some semiclassical Gen Rel derived from LQG.
    and he EXPLAINS for the first time why naked do not exist.

    he says that in the situation where using classical Einstein Gen Rel you would get a naked, in that situation a quantum effect causes the bugger to evaporate before the singularity can form

    so Joshi is better than Hawking. Sir Stephen didnt know how to prove they couldnt exist so he made a bet with Thorne that they couldnt and later on a computer model showed they could (in standard classical Gen Rel) so he had to PAY UP, and because he didnt know how to prove they didnt exist he went and made up "cosmic censorship conjecture", that says they dont exist.

    Joshi says look it is no problem if you use Loop to quantize Gen Rel then whatever would have formed a naked classically is now going to evaporate in a gammaray burst.

    We need to catch up with the world. Bombay is now called Mumbai.
    Madras is now called Chennai.
    they have institutes at these places where as far as I can see some of the work is more interesting than what people like Witten do at Princeton.
    Personally I find that a bit shocking.
     
    Last edited: Jul 2, 2005
  11. Jul 2, 2005 #10
    The actual point of a singularity has no dimension. A manifold cannot be constructed of a single point. So by definition a singularity does not exit. There is no need to prove it; it is true by definition.
     
  12. Jul 2, 2005 #11

    wolram

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    Ah the proofless prof strikes again.

    hawking have invented an extra postulate called "cosmic censorship" which ASSUMES without proof that they do not exist.
     
  13. Jul 2, 2005 #12

    selfAdjoint

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    A space with a singularity is not a manifold, because every sufficiently small neighborhood of a manifold is homeomrphic to Rn. Pseudo-manifolds have every small neighborhood homeomorphic to n-fold Minkowski space. A neighborhood with a singularity in it is not so homeomorphic.

    But who says spacetime has to be everywhere a manifold? Not Einstein, since his GR math does admit singularities.
     
  14. Jul 2, 2005 #13

    George Jones

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    As I understand things (and I might be wrong), singular spacetimes are manifolds (without boundary). Singular spacetimes are, in some sense incomplete - usually, but not always, geodesically incomplete. This does not destroy their manifold structure.

    I am not sure there is agreement on a precise definition of "singularity", but often singualrities are defined as boundary points that "want to be" in the manifold, but aren't.

    Also, your relation between general spacetime manifolds and Minkowski space doesn't look quite right.

    The term "homeomorphism" refers only to topological srtucture, not to other things like differentiable or metric structure. If you mean homeomorphism to refer only to topology, than things are almost OK, but if, as I think, you want homeomorphism to include also (pseudo)metric structure, than what you say is not correct.

    Every point in an n-dimensional topological manifold is contained in an open neighbourbood that is homeomorphic to an open subset of R^n. As topological spaces, (all of) Minkowki space is homeomorphic to (all of) R^n. Usually, spacetimes are modeled as topological spaces (together with other structure), so there exist open neighbourhoods of points in any spacetime homeomorphic to open subsets of Minkowski. But if you intend to include metric structure, then the correct term is isometric, not homeomorphic.

    The above stuff about spacetimes is not true with homeomorphic replaced by isometric. If it were, every event in spacetime would be contained in a neighbourhood for which the curvature is zero everywhere in the neighbourhood. This is condradicted by, for example, Schwarzschild spacetime. The curvature tensor in nowhere zero, not even at any isolated points, for Schwarzschild.

    It is true that for any point p in spacetime, it is possible to find a coordinate system such that at p: 1) the metric tensor takes on the Minkowski form; 2) all the first partial derivatives with repect to these special coordinates of the metric tensor vanish.

    Because higher order partials don't necessarily vanish, as one moves away from p, one, in general, moves away from something that looks like Minkowski space. So it's only at individual points that spacetime looks like Minkowski space, not in neighbourhoods.

    I agree that spacetime doesn't have to be everywhere a manifold, but maybe not for the same reasons. :smile:

    Regards,
    George :smile:
     
  15. Jul 3, 2005 #14

    selfAdjoint

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    No, the PUNCTURED manifold - the original one with the point of singularity removed - is a manfold without boundary (non-compact) near the point of singularity, but the original space with a singularity is not a manifold, by definition.
     
  16. Jul 3, 2005 #15

    George Jones

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    I'm not sure what you mean - could you give a specific examples.

    I used "without boundary" to mean something other than "non-compact". For example , as a topological space, the Lie group SU(3) is S^3, which is compact, but SU(3) is a manifold without boundary.

    Any spacetime manifold that is compact has problems with causality, i.e., contains closed timelike curves.

    Consider 4-dimensional Minkowski spacetime (M , g), where M is the differentiable manifold part and g is the standard Minkowski metric.This is a non-singular spacetime that is a manifold without boundary. Let M' be M with a point removed. M' is also a manifold without boundary, but (M' g'), where g' is g restricted to M', is a singular spacetime. Let M'' be M with a line removed. M'' is a manifold without boundary, and (M'' g''), where g'' is g restricted to M'', is a singular spacetime.

    Not only that, because differentiable structure is largely independent of metric structure, there are Lorentzian metrics different form g' and g'' that can be assigned to the differentiable manifolds M' and M'' that turn them into completely different spacetimes. As a topological space, M' = S^3 x R, which is the underlying space for a closed Friedmann-Robertson-Walker universe (lambda = 0). As a topological space, M'' = S^2 x R^2, which is the underlying space for the maximally extended Schwarzschild spacetime.

    Regards,
    George
     
  17. Jul 3, 2005 #16

    selfAdjoint

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    Consider a meromorphic function in the complex plane with a single pole at some value z_0. The function is analytic in the whole plane minus that point; the set of points where it is analytic is a manifold (homeomorphic to an annulus), but it is not the plane.
     
  18. Jul 4, 2005 #17
    Marcus, going throught the posting and links you have provided (even in the 41 paper link?), I could not find the most relevant paper by T.P.Singh, so here is a link:http://arxiv.org/abs/gr-qc/9805066

    This is as good as it gets :biggrin:
     
  19. Jul 4, 2005 #18

    marcus

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    Thanks, Spin_Network, I will remedy the omission

    http://arxiv.org/abs/gr-qc/9805066
    Gravitational Collapse, Black Holes and Naked Singularities
    T. P. Singh
    17 pages. Based on a talk given at the Discussion Workshop on Black Holes, Bangalore, 9-12 Dec. 1997

    "This article gives an elementary review of gravitational collapse and the cosmic censorship hypothesis. Known models of collapse resulting in the formation of black holes and naked singularities are summarized. These models, when taken together, suggest that the censorship hypothesis may not hold in classical general relativity. The nature of the quantum processes that take place near a naked singularity, and their possible implication for observations, is briefly discussed."

    I find i have the downloaded PDF file here on my desktop, but must have neglected to post the article. It is very fine. a beautiful and thoughtful review, followed by enlightening discussion with the audience like this exchange on page 16:

    Tariq Shahbaz: "How much energy would you expect to be released in the formation of a naked singularity?"

    T. P. Singh: "At this stage, it is difficult to give a precise answer to this question, and the answer will also be model dependent. A few general remarks can be made. The energy release will come not only because of the naked singularity, but also because of the high curvature regions surrounding it. Let there be a visible region of mass M, which has curvature high enough so that the associated curvature length scale is comparable to the Compton wavelength of some typical elementary particles. Then one can expect almost the entire mass M to be converted by pair creation into the energy released during collapse."

    BTW here is a picture of T.P. Singh, his homepage at Tata Institute (Mumbai).
    http://www.tifr.res.in/~tpsingh/
    It lists his research interests as Gen Rel, Quantum Gravity, Cosmology. It says he got his PhD at Tata in 1989 (same year Renate Loll's degree at London Imperial College). rough guess both TP and Renate born in 1962.

    have to distinguish Singhs---T.P. is Tejinder Singh at Tata Institute----Parampreet Singh is a postdoc at Penn State, very good in LQC and associated phenomenology, but quite a bit younger.
     
    Last edited: Jul 4, 2005
  20. Jul 4, 2005 #19

    George Jones

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    I have pent some time (but still note enough!) reading and thinking about singularities and global methods in general relativity, but I have spent an embarrassingly small amount of time looking at the theory of complex functions, which is an extremely important area. Consequently, right now I'm not up speed sufficiently to make comparisons between the singularities in these two areas.

    I hope to find the time to look at your example in more detail, but I move quite slowly at stuff like this.

    Regards,
    George
     
  21. Jul 7, 2005 #20

    marcus

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    hi George, hope you are still around and that you possibly may still be interested in this blowing up of wannabe naked singularities
    that was discussed in the lead paper in this thread.

    there is accumulating evidence that LQC (loop quantum cosmology) may be consistent with classical cosmology, and could be a good quantization of classical which will eventually check out with observation.

    for now it is certainly very iffy, but evidence accumulates bit by bit

    LQC is a symmetry reduced "toy" version of LQG, like the Friedman equation cosmology model is a symmetry reduced simplification of the full einstein eqn.

    I suppose it is possible that LQG could be wrong but this simplification of it to cosmology, LQC, could be right, at least provisionally might pass some of the tests.

    Anyway another Parampreet Singh paper came out today. Another piece of the puzzle:
    http://arxiv.org/abs/gr-qc/0507029
    Semi-classical States, Effective Dynamics and Classical Emergence in Loop Quantum Cosmology
    Parampreet Singh, Kevin Vandersloot
    8 pages, 4 figures
    IGPG-05/7-1, AEI-2005-122

    "We construct physical semi-classical states annihilated by the Hamiltonian constraint operator in the framework of loop quantum cosmology as a method of systematically determining the regime and validity of the semi-classical limit of the quantum theory. Our results indicate that the evolution can be effectively described using continuous classical equations of motion with non-perturbative corrections down to near the Planck scale below which the universe can only be described by the discrete quantum constraint. These results, for the first time, provide concrete evidence of the emergence of classicality in loop quantum cosmology and also clearly demarcate the domain of validity of different effective theories. We prove that discrete quantum geometry effects may become very significant and lead to various new phenomenological applications. Furthermore the understanding of semi-classical states allows for a framework for interpreting the quantum wavefunctions and understanding questions of a semi-classical nature within the quantum theory of loop quantum cosmology."

    I see it has a Penn State report number (Singh has been a postdoc at Ashtekar's Institute there) but also a AEI-Potsdam report number. One of the two authors must also be at the Potsdam MPI Albert Einstein Institute, where Bojowald is.
     
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