Abstract
We discuss how long strings can arise at the stretched horizon and how they can account for the Bekenstein-Hawking entropy. We use the thermal scalar field theory to derive the asymptotic density of states and corresponding stress tensor of a microcanonical long string gas in Rindler space. We show that the equality of the Hagedorn and Hawking temperatures gives rise to the tree-level entropy of large black holes in accordance with the Bekenstein-Hawking-Wald formula.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
G. ’t Hooft, On the quantum structure of a black hole, Nucl. Phys. B 256 (1985) 727 [INSPIRE].
L. Susskind, Some speculations about black hole entropy in string theory, in The black hole, C. Teitelboim ed., World Scientific, Singapore (1998), pg. 118 [hep-th/9309145] [INSPIRE].
M. Hewitt, Strings and gravitational collapse, Phys. Lett. B 309 (1993) 264 [INSPIRE].
K.S. Thorne, R.H. Price and D.A. Macdonald, Black holes: the membrane paradigm, Yale Univ. Pr., New Haven U.S.A. (1986) [INSPIRE].
A. Strominger and C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy, Phys. Lett. B 379 (1996) 99 [hep-th/9601029] [INSPIRE].
A. Giveon and N. Itzhaki, String theory versus black hole complementarity, JHEP 12 (2012) 094 [arXiv:1208.3930] [INSPIRE].
A. Giveon and N. Itzhaki, String theory at the tip of the cigar, JHEP 09 (2013) 079 [arXiv:1305.4799] [INSPIRE].
A. Giveon, N. Itzhaki and J. Troost, Lessons on black holes from the elliptic genus, JHEP 04 (2014) 160 [arXiv:1401.3104] [INSPIRE].
A. Giveon, N. Itzhaki and J. Troost, The black hole interior and a curious sum rule, JHEP 03 (2014) 063 [arXiv:1311.5189] [INSPIRE].
E.J. Martinec, The Cheshire cap, JHEP 03 (2015) 112 [arXiv:1409.6017] [INSPIRE].
E. Halyo, Black holes as conformal field theories on horizons, arXiv:1502.01979 [INSPIRE].
E. Halyo, Horizon conformal field theories from AdS 2 black holes, arXiv:1503.07808 [INSPIRE].
A. Giveon, N. Itzhaki and D. Kutasov, Stringy horizons, JHEP 06 (2015) 064 [arXiv:1502.03633] [INSPIRE].
G. Giribet and A. Ranjbar, Screening stringy horizons, Eur. Phys. J. C 75 (2015) 490 [arXiv:1504.05044] [INSPIRE].
R. Ben-Israel, A. Giveon, N. Itzhaki and L. Liram, Stringy horizons and UV/IR mixing, JHEP 11 (2015) 164 [arXiv:1506.07323] [INSPIRE].
E. Silverstein, Backdraft: string creation in an old Schwarzschild black hole, arXiv:1402.1486 [INSPIRE].
M. Dodelson and E. Silverstein, String-theoretic breakdown of effective field theory near black hole horizons, arXiv:1504.05536 [INSPIRE].
M. Dodelson and E. Silverstein, Longitudinal nonlocality in the string S-matrix, arXiv:1504.05537 [INSPIRE].
T.G. Mertens, H. Verschelde and V.I. Zakharov, Random walks in Rindler spacetime and string theory at the tip of the cigar, JHEP 03 (2014) 086 [arXiv:1307.3491] [INSPIRE].
D. Mitchell and N. Turok, Statistical mechanics of cosmic strings, Phys. Rev. Lett. 58 (1987) 1577 [INSPIRE].
D. Mitchell and N. Turok, Statistical properties of cosmic strings, Nucl. Phys. B 294 (1987) 1138 [INSPIRE].
T.G. Mertens, H. Verschelde and V.I. Zakharov, Near-Hagedorn thermodynamics and random walks — extensions and examples, JHEP 11 (2014) 107 [arXiv:1408.6999] [INSPIRE].
E. Alvarez and M.A.R. Osorio, Superstrings at finite temperature, Phys. Rev. D 36 (1987) 1175 [INSPIRE].
J. Polchinski, Evaluation of the one loop string path integral, Commun. Math. Phys. 104 (1986) 37 [INSPIRE].
J.J. Atick and E. Witten, The Hagedorn transition and the number of degrees of freedom of string theory, Nucl. Phys. B 310 (1988) 291 [INSPIRE].
G.T. Horowitz and J. Polchinski, Selfgravitating fundamental strings, Phys. Rev. D 57 (1998) 2557 [hep-th/9707170] [INSPIRE].
J.L.F. Barbon and E. Rabinovici, Touring the Hagedorn ridge, in From fields to strings, vol. 3, M. Shifman et al. eds., World Scientific, Singapore (1973)–(2008) [hep-th/0407236] [INSPIRE].
M. Kruczenski and A. Lawrence, Random walks and the Hagedorn transition, JHEP 07 (2006) 031 [hep-th/0508148] [INSPIRE].
T.G. Mertens, H. Verschelde and V.I. Zakharov, Near-Hagedorn thermodynamics and random walks: a general formalism in curved backgrounds, JHEP 02 (2014) 127 [arXiv:1305.7443] [INSPIRE].
T.G. Mertens, H. Verschelde and V.I. Zakharov, On the relevance of the thermal scalar, JHEP 11 (2014) 157 [arXiv:1408.7012] [INSPIRE].
T.G. Mertens, H. Verschelde and V.I. Zakharov, Perturbative string thermodynamics near black hole horizons, JHEP 06 (2015) 167 [arXiv:1410.8009] [INSPIRE].
L. Susskind and J. Uglum, Black hole entropy in canonical quantum gravity and superstring theory, Phys. Rev. D 50 (1994) 2700 [hep-th/9401070] [INSPIRE].
S. Carlip and C. Teitelboim, The off-shell black hole, Class. Quant. Grav. 12 (1995) 1699 [gr-qc/9312002] [INSPIRE].
T.G. Mertens, H. Verschelde and V.I. Zakharov, String partition functions in Rindler space and maximal acceleration, arXiv:1511.00560 [INSPIRE].
F. Larsen and F. Wilczek, Internal structure of black holes, Phys. Lett. B 375 (1996) 37 [hep-th/9511064] [INSPIRE].
J.M. Maldacena, Statistical entropy of near extremal five-branes, Nucl. Phys. B 477 (1996) 168 [hep-th/9605016] [INSPIRE].
E. Halyo, A. Rajaraman and L. Susskind, Braneless black holes, Phys. Lett. B 392 (1997) 319 [hep-th/9605112] [INSPIRE].
A.A. Tseytlin, Extremal black hole entropy from conformal string σ-model, Nucl. Phys. B 477 (1996) 431 [hep-th/9605091] [INSPIRE].
L. Susskind, Strings, black holes and Lorentz contraction, Phys. Rev. D 49 (1994) 6606 [hep-th/9308139] [INSPIRE].
G.T. Horowitz and J. Polchinski, A correspondence principle for black holes and strings, Phys. Rev. D 55 (1997) 6189 [hep-th/9612146] [INSPIRE].
W.H. Zurek and K.S. Thorne, Statistical mechanical origin of the entropy of a rotating, charged black hole, Phys. Rev. Lett. 54 (1985) 2171 [INSPIRE].
C.W. Misner, K.S. Thorne and J.A. Wheeler, Gravitation, W.H. Freeman, San Francisco U.S.A. (1973) [INSPIRE].
V.P. Frolov and K.S. Thorne, Renormalized stress-energy tensor near the horizon of a slowly evolving, rotating black hole, Phys. Rev. D 39 (1989) 2125 [INSPIRE].
S.W. Hawking and H.S. Reall, Charged and rotating AdS black holes and their CFT duals, Phys. Rev. D 61 (2000) 024014 [hep-th/9908109] [INSPIRE].
E. Winstanley, On classical superradiance in Kerr-Newman-anti-de Sitter black holes, Phys. Rev. D 64 (2001) 104010 [gr-qc/0106032] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1505.04025
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Mertens, T.G., Verschelde, H. & Zakharov, V.I. The long string at the stretched horizon and the entropy of large non-extremal black holes. J. High Energ. Phys. 2016, 41 (2016). https://doi.org/10.1007/JHEP02(2016)041
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2016)041