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Monsters, Black Holes and Entropy

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Quantum Aspects of Black Holes

Part of the book series: Fundamental Theories of Physics ((FTPH,volume 178))

Abstract

Classical general relativity allows for compact objects—“monsters”—with more entropy than black holes of equal mass. We construct examples of such configurations and describe their general properties. Monsters are problematic for certain versions of the AdS/CFT duality, and possibly even for the application of statistical mechanics to quantum gravity. It is possible that they are somehow excluded from the Hilbert space of quantum gravity, although this would be in contrast to the usual case in which coarse-grained, semiclassical configurations have (many) quantum counterparts.

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Notes

  1. 1.

    Note, we need to restrict the size of the object as well as its total energy. An object with fixed total energy \(E = T^4 R^3\), but no restriction on \(R\), can have infinite entropy: we can take \(R\rightarrow \infty \) and \(T\rightarrow 0\) with \(E\) fixed, so that \(S = T^3 R^3 = E / T \rightarrow \infty \).

  2. 2.

    Of course, it is also possible that the initial pure state is atypical and subsequent dynamics somehow keeps the state in a very atypical region of the Hilbert space over very long time scales, so that the highly entropic configurations are essentially never sampled. In that case one cannot deduce the thermodynamic properties of the system from the concentration of measure phenomenon (i.e., typicality) alone: the system does not actually reach ultimate equilibrium.

References

  1. Marolf, D.: Gen. Rel. Grav. 41, 903 (2009). arXiv:0810.4886 [gr-qc]

  2. Hossenfelder, S., Smolin, l.: Phys. Rev. D 81, 064009 (2010). arXiv:0901.3156 [gr-qc]

  3. Strominger, A., Vafa, C.: Phys. Lett. B 379, 99 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  4. Maldacena, J.M., Strominger, A., Witten, E.: JHEP 12, 002 (1997)

    Article  ADS  Google Scholar 

  5. Hawking, S.W.: Commun. Math. Phys. 43, 199 (1975)

    Article  ADS  Google Scholar 

  6. Bekenstein, J.D.: Phys. Rev. D 7, 2333 (1973)

    Article  ADS  MathSciNet  Google Scholar 

  7. Jacobson, T. arXiv:gr-qc/9908031

  8. Hooft, G.’t.: In:Ali et al. (eds.) Salamfestschrift. World Scientific (1994)

    Google Scholar 

  9. Thorne, K.S.: In: Klauder, J.R. (eds.) Magic Without Magic. Freeman (1973)

    Google Scholar 

  10. Eardley, D.M., Giddings, S.B.: Phys. Rev. D 66, 044011 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  11. Hsu, S.D.H.: Phys. Lett. B 555, 92 (2003)

    Article  ADS  Google Scholar 

  12. Hawking, S.W.: Phys. Rev. D 14, 2460 (1976)

    Article  ADS  MathSciNet  Google Scholar 

  13. Hsu, S.D.H.: Phys. Lett. B 644, 67 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  14. Hsu, S.D.H. arXiv:gr-qc/9801106

  15. Sorkin, R.D., Wald, R.M., Zhang, Z.J.: Gen. Rel. Grav. 13, 1127 (1981)

    Article  ADS  Google Scholar 

  16. Hsu, S.D.H., Reeb, D.: Phys. Lett. B 658, 244 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  17. Aharony, O., Gubser, S.S., Maldacena, J.M., Ooguri, H., Oz, Y.: Phys. Rept. 323, 183 (2000)

    Article  ADS  Google Scholar 

  18. Bousso, R.: JHEP 07, 004 (1999)

    Article  ADS  Google Scholar 

  19. Flanagan, E.E., Marolf, D., Wald, R.M.: Phys. Rev. D 62, 084035 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  20. Hsu, S.D.H., Reeb, D.: Class. Quant. Grav. 25, 235007 (2008)

    Article  ADS  Google Scholar 

  21. Popescu, S., Short, A.J., Winter, A.: Nat. Phys. 2, 754 (2006). See also. arXiv:quant-ph/0511225

  22. Gemmer, J., Michel, M., Mahler, G.: Quantum Thermodynamics: Emergence of Thermodynamic Behavior Within Composite Quantum Systems, Springer, Berlin (2004)

    Google Scholar 

  23. Ledoux, M.: The Concentration of Measure Phenomenon. American Mathematical Society, Providence (2001)

    Google Scholar 

  24. Linden, N., Popescu, S., Short, A.J., Winter, A. arXiv:0812.2385 [quant-ph]

  25. Hayden, P., Leung, D.W., Winter, A.: Comm. Math. Phys. 265, 95 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  26. Misner, C.W., Thorne, K.S., Wheeler, J. A.: Gravitation. Freeman (1973)

    Google Scholar 

  27. Kiefer, C.: Quantum Gravity, 2nd edn. Oxford University Press, Oxford (2007)

    Google Scholar 

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Acknowledgments

The author acknowledges support from the Office of the Vice-President for Research and Graduate Studies at Michigan State University.

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Authors and Affiliations

  1. Department of Physics and Astronomy, Michigan State University, East Lansing, MI, 48824, USA

    Stephen D. H. Hsu

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  1. Stephen D. H. Hsu
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Correspondence to Stephen D. H. Hsu .

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Editors and Affiliations

  1. Department of Physics & Astronomy, University of Sussex, Brighton, United Kingdom

    Xavier Calmet

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Hsu, S.D.H. (2015). Monsters, Black Holes and Entropy. In: Calmet, X. (eds) Quantum Aspects of Black Holes. Fundamental Theories of Physics, vol 178. Springer, Cham. https://doi.org/10.1007/978-3-319-10852-0_4

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