Abstract
The correspondence principle between strings and black holes is a general framework for matching black holes and massive states of fundamental strings at a point where their physical properties (such as mass, entropy and temperature) smoothly agree with each other. This correspondence becomes puzzling when attempting to include rotation: At large enough spins, there exist degenerate string states that seemingly cannot be matched to any black hole. Conversely, there exist black holes with arbitrarily large spins that cannot correspond to any single-string state. We discuss in detail the properties of both types of objects and find that a correspondence that resolves the puzzles is possible by adding dynamical features and non-stationary configurations to the picture. Our scheme incorporates all black hole and string phases as part of the correspondence, save for one outlier which remains enigmatic: the near-extremal Kerr black hole. Along the way, we elaborate on general aspects of the correspondence that have not been emphasized before.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
M.B. Green, J.H. Schwarz and E. Witten, Superstring Theory. Vol. 1: Introduction, Cambridge University Press (1988).
L. Susskind, Some speculations about black hole entropy in string theory, hep-th/9309145 [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].
J.M. Bardeen and G.T. Horowitz, The extreme Kerr throat geometry: A vacuum analog of AdS2 × S2, Phys. Rev. D 60 (1999) 104030 [hep-th/9905099] [INSPIRE].
J.G. Russo and L. Susskind, Asymptotic level density in heterotic string theory and rotating black holes, Nucl. Phys. B 437 (1995) 611 [hep-th/9405117] [INSPIRE].
R. Emparan and H.S. Reall, A rotating black ring solution in five-dimensions, Phys. Rev. Lett. 88 (2002) 101101 [hep-th/0110260] [INSPIRE].
R.C. Myers and M.J. Perry, Black Holes in Higher Dimensional Space-Times, Annals Phys. 172 (1986) 304 [INSPIRE].
M. Karliner, I.R. Klebanov and L. Susskind, Size and Shape of Strings, Int. J. Mod. Phys. A 3 (1988) 1981 [INSPIRE].
L. Susskind, Black Hole-String Correspondence, arXiv:2110.12617 [INSPIRE].
C.G. Callan Jr., R.C. Myers and M.J. Perry, Black Holes in String Theory, Nucl. Phys. B 311 (1989) 673 [INSPIRE].
M.J. Bowick, L. Smolin and L.C.R. Wijewardhana, Role of String Excitations in the Last Stages of Black Hole Evaporation, Phys. Rev. Lett. 56 (1986) 424 [INSPIRE].
Y. Chen, J. Maldacena and E. Witten, On the black hole/string transition, JHEP 01 (2023) 103 [arXiv:2109.08563] [INSPIRE].
G.T. Horowitz and J. Polchinski, Selfgravitating fundamental strings, Phys. Rev. D 57 (1998) 2557 [hep-th/9707170] [INSPIRE].
T. Damour and G. Veneziano, Selfgravitating fundamental strings and black holes, Nucl. Phys. B 568 (2000) 93 [hep-th/9907030] [INSPIRE].
R. Brustein and Y. Zigdon, Black hole entropy sourced by string winding condensate, JHEP 10 (2021) 219 [arXiv:2107.09001] [INSPIRE].
Y. Matsuo, Fluid model of a black hole-string transition, Phys. Rev. D 107 (2023) 126003 [arXiv:2205.15976] [INSPIRE].
E.Y. Urbach, String stars in anti de Sitter space, JHEP 04 (2022) 072 [arXiv:2202.06966] [INSPIRE].
B. Balthazar, J. Chu and D. Kutasov, On Small Black Holes in String Theory, arXiv:2210.12033 [INSPIRE].
E.Y. Urbach, The black hole/string transition in AdS3 and confining backgrounds, JHEP 09 (2023) 156 [arXiv:2303.09567] [INSPIRE].
J.E. Santos and Y. Zigdon, in progress.
I. Bena et al., in progress.
D. Amati and J.G. Russo, Fundamental strings as black bodies, Phys. Lett. B 454 (1999) 207 [hep-th/9901092] [INSPIRE].
R. Iengo and J.G. Russo, Handbook on string decay, JHEP 02 (2006) 041 [hep-th/0601072] [INSPIRE].
R. Emparan, T. Harmark, V. Niarchos and N.A. Obers, Essentials of Blackfold Dynamics, JHEP 03 (2010) 063 [arXiv:0910.1601] [INSPIRE].
H. Elvang, R. Emparan and A. Virmani, Dynamics and stability of black rings, JHEP 12 (2006) 074 [hep-th/0608076] [INSPIRE].
J.E. Santos and B. Way, Neutral Black Rings in Five Dimensions are Unstable, Phys. Rev. Lett. 114 (2015) 221101 [arXiv:1503.00721] [INSPIRE].
P. Figueras, M. Kunesch and S. Tunyasuvunakool, End Point of Black Ring Instabilities and the Weak Cosmic Censorship Conjecture, Phys. Rev. Lett. 116 (2016) 071102 [arXiv:1512.04532] [INSPIRE].
R. Emparan and R.C. Myers, Instability of ultra-spinning black holes, JHEP 09 (2003) 025 [hep-th/0308056] [INSPIRE].
O.J.C. Dias et al., Instability and new phases of higher-dimensional rotating black holes, Phys. Rev. D 80 (2009) 111701 [arXiv:0907.2248] [INSPIRE].
M. Shibata and H. Yoshino, Bar-mode instability of rapidly spinning black hole in higher dimensions: Numerical simulation in general relativity, Phys. Rev. D 81 (2010) 104035 [arXiv:1004.4970] [INSPIRE].
Ó.J.C. Dias, G.S. Hartnett and J.E. Santos, Quasinormal modes of asymptotically flat rotating black holes, Class. Quant. Grav. 31 (2014) 245011 [arXiv:1402.7047] [INSPIRE].
H. Bantilan, P. Figueras, M. Kunesch and R. Panosso Macedo, End point of nonaxisymmetric black hole instabilities in higher dimensions, Phys. Rev. D 100 (2019) 086014 [arXiv:1906.10696] [INSPIRE].
R. Emparan et al., The Phase Structure of Higher-Dimensional Black Rings and Black Holes, JHEP 10 (2007) 110 [arXiv:0708.2181] [INSPIRE].
Ó.J.C. Dias, J.E. Santos and B. Way, Rings, Ripples, and Rotation: Connecting Black Holes to Black Rings, JHEP 07 (2014) 045 [arXiv:1402.6345] [INSPIRE].
R. Emparan, P. Figueras and M. Martinez, Bumpy black holes, JHEP 12 (2014) 072 [arXiv:1410.4764] [INSPIRE].
R. Emparan and H.S. Reall, Black Holes in Higher Dimensions, Living Rev. Rel. 11 (2008) 6 [arXiv:0801.3471] [INSPIRE].
J. Armas and T. Harmark, Black Holes and Biophysical (Mem)-branes, Phys. Rev. D 90 (2014) 124022 [arXiv:1402.6330] [INSPIRE].
R. Gregory and R. Laflamme, Black strings and p-branes are unstable, Phys. Rev. Lett. 70 (1993) 2837 [hep-th/9301052] [INSPIRE].
T. Andrade, R. Emparan and D. Licht, Rotating black holes and black bars at large D, JHEP 09 (2018) 107 [arXiv:1807.01131] [INSPIRE].
T. Andrade, R. Emparan, D. Licht and R. Luna, Black hole collisions, instabilities, and cosmic censorship violation at large D, JHEP 09 (2019) 099 [arXiv:1908.03424] [INSPIRE].
T. Harmark, V. Niarchos and N.A. Obers, Instabilities of black strings and branes, Class. Quant. Grav. 24 (2007) R1 [hep-th/0701022] [INSPIRE].
T. Andrade, P. Figueras and U. Sperhake, Evidence for violations of Weak Cosmic Censorship in black hole collisions in higher dimensions, JHEP 03 (2022) 111 [arXiv:2011.03049] [INSPIRE].
D.N. Page, Particle Emission Rates from a Black Hole: Massless Particles from an Uncharged, Nonrotating Hole, Phys. Rev. D 13 (1976) 198 [INSPIRE].
L.V. Iliesiu and G.J. Turiaci, The statistical mechanics of near-extremal black holes, JHEP 05 (2021) 145 [arXiv:2003.02860] [INSPIRE].
J.J. Blanco-Pillado, R. Emparan and A. Iglesias, Fundamental Plasmid Strings and Black Rings, JHEP 01 (2008) 014 [arXiv:0712.0611] [INSPIRE].
J.J. Blanco-Pillado, A. Iglesias and W. Siegel, On Semiclassical Limits of String States, Phys. Lett. B 655 (2007) 284 [arXiv:0706.0731] [INSPIRE].
J.L. Manes, Portrait of the string as a random walk, JHEP 03 (2005) 070 [hep-th/0412104] [INSPIRE].
T. Matsuo, Massless radiation from heavy rotating string and Kerr/string correspondence, Nucl. Phys. B 827 (2010) 217 [arXiv:0909.1617] [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].
N. Čeplak, R. Emparan, A. Puhm and M. Tomašević, to appear.
V.P. Frolov, S. Hendy and J.P. De Villiers, Rigidly rotating strings in stationary axisymmetric space-times, Class. Quant. Grav. 14 (1997) 1099 [hep-th/9612199] [INSPIRE].
M. Snajdr and V.P. Frolov, Capture and critical scattering of a long cosmic string by a rotating black hole, Class. Quant. Grav. 20 (2003) 1303 [gr-qc/0211018] [INSPIRE].
S. Kinoshita, T. Igata and K. Tanabe, Energy extraction from Kerr black holes by rigidly rotating strings, Phys. Rev. D 94 (2016) 124039 [arXiv:1610.08006] [INSPIRE].
T. Igata, H. Ishihara, M. Tsuchiya and C.-M. Yoo, Rigidly Rotating String Sticking in a Kerr Black Hole, Phys. Rev. D 98 (2018) 064021 [arXiv:1806.09837] [INSPIRE].
H. Xing, Y. Levin, A. Gruzinov and A. Vilenkin, Spinning black holes as cosmic string factories, Phys. Rev. D 103 (2021) 083019 [arXiv:2011.00654] [INSPIRE].
H. Deng, A. Gruzinov, Y. Levin and A. Vilenkin, Simulating cosmic string loop captured by a rotating black hole, Phys. Rev. D 107 (2023) 123016 [arXiv:2303.02726] [INSPIRE].
M. Guica, T. Hartman, W. Song and A. Strominger, The Kerr/CFT Correspondence, Phys. Rev. D 80 (2009) 124008 [arXiv:0809.4266] [INSPIRE].
G. Compère, The Kerr/CFT correspondence and its extensions, Living Rev. Rel. 15 (2012) 11 [arXiv:1203.3561] [INSPIRE].
R. Emparan, Rotating circular strings, and infinite nonuniqueness of black rings, JHEP 03 (2004) 064 [hep-th/0402149] [INSPIRE].
R. Emparan, M. Sanchez-Garitaonandia and M. Tomašević, in progress.
M.M. Sheikh-Jabbari and H. Yavartanoo, EVH Black Holes, AdS3 Throats and EVH/CFT Proposal, JHEP 10 (2011) 013 [arXiv:1107.5705] [INSPIRE].
M.M. Caldarelli, R. Emparan and B. Van Pol, Higher-dimensional Rotating Charged Black Holes, JHEP 04 (2011) 013 [arXiv:1012.4517] [INSPIRE].
R. Emparan, T. Harmark, V. Niarchos and N.A. Obers, Blackfolds in Supergravity and String Theory, JHEP 08 (2011) 154 [arXiv:1106.4428] [INSPIRE].
R. Emparan and G.T. Horowitz, Microstates of a Neutral Black Hole in M Theory, Phys. Rev. Lett. 97 (2006) 141601 [hep-th/0607023] [INSPIRE].
G.T. Horowitz and M.M. Roberts, Counting the Microstates of a Kerr Black Hole, Phys. Rev. Lett. 99 (2007) 221601 [arXiv:0708.1346] [INSPIRE].
Acknowledgments
We thank Iosif Bena, Yiming Chen, Veronika Hubeny, Luca Iliesiu, Raghu Mahajan, David Mateos, Mukund Rangamani, Jorge Santos and Yoav Zigdon for conversations. RE is grateful to Gary Horowitz and Rob Myers for early discussions on this topic. The work of NČ is supported by the ERC Grant 787320 – QBH Structure. RE is supported by MICINN grant PID2019-105614GB-C22, AGAUR grant 2017-SGR 754, and State Research Agency of MICINN through the “Unit of Excellence Maria de Maeztu 2020-2023” award to the Institute of Cosmos Sciences (CEX2019-000918-M). AP and MT are supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 852386).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2307.03573
Rights and permissions
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.
About this article
Cite this article
Čeplak, N., Emparan, R., Puhm, A. et al. The correspondence between rotating black holes and fundamental strings. J. High Energ. Phys. 2023, 226 (2023). https://doi.org/10.1007/JHEP11(2023)226
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2023)226