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Higher Spin Black Holes

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Modifications of Einstein's Theory of Gravity at Large Distances

Part of the book series: Lecture Notes in Physics ((LNP,volume 892))

Abstract

We review some relevant results in the context of higher spin black holes in three-dimensional spacetimes, focusing on their asymptotic behaviour and thermodynamic properties. For simplicity, we mainly discuss the case of gravity nonminimally coupled to spin-three fields, being nonperturbatively described by a Chern–Simons theory of two independent \(\mathit{sl}\left (3, \mathbb{R}\right )\) gauge fields. Since the analysis is particularly transparent in the Hamiltonian formalism, we provide a concise discussion of their basic aspects in this context; and as a warming up exercise, we briefly analyze the asymptotic behaviour of pure gravity, as well as the BTZ black hole and its thermodynamics, exclusively in terms of gauge fields. The discussion is then extended to the case of black holes endowed with higher spin fields, briefly signaling the agreements and discrepancies found through different approaches. We conclude explaining how the puzzles become resolved once the fall off of the fields is precisely specified and extended to include chemical potentials, in a way that it is compatible with the asymptotic symmetries. Hence, the global charges become completely identified in an unambiguous way, so that different sets of asymptotic conditions turn out to contain inequivalent classes of black hole solutions being characterized by a different set of global charges.

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References

  1. P. Van Nieuwenhuizen, “Supergravity.” Phys. Rept. 68, 189 (1981)

    Article  ADS  Google Scholar 

  2. X. Bekaert, N. Boulanger, P. Sundell, How higher-spin gravity surpasses the spin two barrier: no-go theorems versus yes-go examples. Rev. Mod. Phys. 84, 987 (2012).[arXiv:1007.0435 [hep-th]]

    Google Scholar 

  3. C. Aragone, S. Deser, Consistency problems of hypergravity. Phys. Lett. B 86, 161 (1979)

    Article  ADS  MathSciNet  Google Scholar 

  4. M.A. Vasiliev, “Consistent equation for interacting gauge fields of all spins in (3 + 1)-dimensions.”Phys. Lett. B 243, 378 (1990)

    Google Scholar 

  5. M.A. Vasiliev, “Nonlinear equations for symmetric massless higher spin fields in (A)dS(d).”Phys. Lett. B 567, 139 (2003). [hep-th/0304049]

    Google Scholar 

  6. X. Bekaert, S. Cnockaert, C. Iazeolla, M.A. Vasiliev, “Nonlinear higher spin theories in various dimensions.” (2005). [hep-th/0503128]

    Google Scholar 

  7. A. Sagnotti, Notes on strings and higher spins. J. Phys. A 46, 214006 (2013). [arXiv:1112.4285 [hep-th]]

    Google Scholar 

  8. M.A. Vasiliev, “Higher-Spin Theory and Space-Time Metamorphoses.” arXiv:1404.1948 [hep-th]

    Google Scholar 

  9. R. Troncoso, J. Zanelli, New gauge supergravity in seven-dimensions and eleven-dimensions. Phys. Rev. D 58, 10170 (1998). [hep-th/9710180]

    Article  MathSciNet  Google Scholar 

  10. M.P. Blencowe, “A consistent interacting massless higher spin field theory in D = (2 + 1).” Class. Quant. Gravity 6, 443 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  11. E. Bergshoeff, M.P. Blencowe, K.S. Stelle, “Area preserving diffeomorphisms and higher spin algebra.” Commun. Math. Phys. 128, 213 (1990)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  12. M.A. Vasiliev, “Higher spin gauge theories in four-dimensions, three-dimensions, and two-dimensions.” Int. J. Mod. Phys. D 5, 763 (1996). [hep-th/9611024]

    Article  ADS  MathSciNet  Google Scholar 

  13. M. Gutperle, P. Kraus, Higher spin black holes. J. High Energy Phys. 1105, 022 (2011). [arXiv:1103.4304 [hep-th]]

    Google Scholar 

  14. A. Castro, E. Hijano, A. Lepage-Jutier, A. Maloney, Black holes and singularity resolution in higher spin gravity. J. High Energy Phys. 1201, 031 (2012). [arXiv:1110.4117 [hep-th]]

    Google Scholar 

  15. M. Henneaux, A. Prez, D. Tempo, R. Troncoso, “Chemical potentials in three-dimensional higher spin anti-de Sitter gravity.” J. High Energy Phys. 1312, 048 (2013). [arXiv:1309.4362 [hep-th]]

    Google Scholar 

  16. C. Bunster, M. Henneaux, A. Prez, D. Tempo, R. Troncoso, “Generalized black holes in three-dimensional spacetime.” JHEP 1405, 031 (2014). [arXiv:1404.3305 [hep-th]]

    Google Scholar 

  17. A. Campoleoni, S. Fredenhagen, S. Pfenninger, S. Theisen, Towards metric-like higher-spin gauge theories in three dimensions. J. Phys. A 46, 214017 (2013). [arXiv:1208.1851 [hep-th]]

    Google Scholar 

  18. J.D. Brown, M. Henneaux, “Central charges in the canonical realization of asymptotic symmetries: an example from three-dimensional gravity.”Commun. Math. Phys. 104, 207 (1986)

    Google Scholar 

  19. M. Banados, C. Teitelboim, J. Zanelli, The black hole in three-dimensional space-time. Phys. Rev. Lett. 69, 1849 (1992). [hep-th/9204099]

    Article  ADS  MATH  MathSciNet  Google Scholar 

  20. M. Banados, M. Henneaux, C. Teitelboim, J. Zanelli, Geometry of the (2+1) black hole. Phys. Rev. D 48, 1506 (1993. [gr-qc/9302012]

    Google Scholar 

  21. M. Henneaux, S.-J. Rey, “Nonlinear W infinity as asymptotic symmetry of three-dimensional higher spin anti-de sitter gravity.” J. High Energy Phys. 1012, 007 (2010). [arXiv:1008.4579 [hep-th]]

    Google Scholar 

  22. A. Campoleoni, S. Fredenhagen, S. Pfenninger, S. Theisen, “Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields.” J. High Energy Phys. 1011, 007 (2010). [arXiv:1008.4744 [hep-th]]

    Google Scholar 

  23. M. Ammon, M. Gutperle, P. Kraus, E. Perlmutter, Spacetime geometry in higher spin gravity. J. High Energy Phys. 1110, 053 (2011). [arXiv:1106.4788 [hep-th]]

    Google Scholar 

  24. A. Prez, D. Tempo, R. Troncoso, “Higher spin gravity in 3D: black holes, global charges and thermodynamics.” Phys. Lett. B 726, 444 (2013). [arXiv:1207.2844 [hep-th]]

    Google Scholar 

  25. A. Pérez, D. Tempo, R. Troncoso, “Higher spin black hole entropy in three dimensions.” J. High Energy Phys. 1304, 143 (2013). [arXiv:1301.0847 [hep-th]]

    Google Scholar 

  26. A.P. Balachandran, G. Bimonte, K.S. Gupta, A. Stern, “Conformal edge currents in Chern-Simons theories.” Int. J. Mod. Phys. A 7, 4655 (1992). [hep-th/9110072]

    Article  ADS  MathSciNet  Google Scholar 

  27. M. Banados, “Global charges in Chern-Simons field theory and the (2+1) black hole.”Phys. Rev. D 52, 5816 (1996). [hep-th/9405171]

    Google Scholar 

  28. S. Carlip, “Conformal field theory, (2 + 1)-dimensional gravity, and the BTZ black hole.”Class. Quant. Gravity 22, R85 (2005). [gr-qc/0503022]

    Google Scholar 

  29. T. Regge, C. Teitelboim, “Role of surface integrals in the Hamiltonian formulation Of general relativity.” Ann. Phys. 88, 286 (1974)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  30. A. Achucarro, P.K. Townsend, “A Chern-Simons action for three-dimensional anti-De Sitter supergravity theories.” Phys. Lett. B 180, 89 (1986)

    Article  ADS  MathSciNet  Google Scholar 

  31. E. Witten, “(2 + 1)-dimensional gravity as an exactly soluble system.” Nucl. Phys. B 311, 46 (1988)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  32. O. Coussaert, M. Henneaux, P. van Driel, The asymptotic dynamics of three-dimensional Einstein gravity with a negative cosmological constant. Class. Quant. Gravity 12, 2961 (1995). [gr-qc/9506019]

    Google Scholar 

  33. S. Carlip, C. Teitelboim, Aspects of black hole quantum mechanics and thermodynamics in (2+1)-dimensions. Phys. Rev. D 51, 622 (1995). [gr-qc/9405070]

    Google Scholar 

  34. J.M. Maldacena, A. Strominger, AdS(3) black holes and a stringy exclusion principle. J. High Energy Phys. 9812, 005 (1998). [hep-th/9804085]

    Article  ADS  MathSciNet  Google Scholar 

  35. H.A. Gonzalez, J. Matulich, M. Pino, R. Troncoso, Asymptotically flat spacetimes in three-dimensional higher spin gravity. J. High Energy Phys. 1309, 016 (2013). [arXiv:1307.5651 [hep-th]]

    Google Scholar 

  36. H. Afshar, A. Bagchi, R. Fareghbal, D. Grumiller, J. Rosseel, “Higher spin theory in 3-dimensional flat space.” Phys. Rev. Lett. 111, 121603 (2013). [arXiv:1307.4768 [hep-th]]

    Google Scholar 

  37. H. A. González, M. Pino, “Boundary dynamics of asymptotically flat 3D gravity coupled to higher spin fields.” arXiv:1403.4898 [hep-th]

    Google Scholar 

  38. D. Grumiller, M. Riegler, J. Rosseel, “Unitarity in three-dimensional flat space higher spin theories.” arXiv:1403.5297 [hep-th]

    Google Scholar 

  39. C. Krishnan, S. Roy, “Higher Spin Resolution of a Toy Big Bang.” Phys. Rev. D 88, 044049 (2013) [arXiv:1305.1277 [hep-th]]

    Google Scholar 

  40. B. Burrington, L.A. Pando Zayas, N. Rombes, “On resolutions of cosmological singularities in higher-spin gravity. ” (2013). [arXiv:1309.1087 [hep-th]]

    Google Scholar 

  41. C. Krishnan, S. Roy, Desingularization of the Milne Universe (2013). [arXiv:1311.7315 [hep-th]]

    Google Scholar 

  42. C. Krishnan, A. Raju, S. Roy, “A Grassmann path from AdS 3 to flat space. ” (2013). arXiv:1312.2941 [hep-th]

    Google Scholar 

  43. G. Compre, W. Song, \(\mathcal{W}\) symmetry and integrability of higher spin black holes. J. High Energy Phys. 1309, 144 (2013). [arXiv:1306.0014 [hep-th]]

    Google Scholar 

  44. G. Compre, J.I. Jottar, W. Song, Observables and microscopic entropy of higher spin black holes. J. High Energy Phys. 1311, 054 (2013). [arXiv:1308.2175 [hep-th]]

    Google Scholar 

  45. M.R. Gaberdiel, T. Hartman, K. Jin, “Higher spin black holes from CFT.” J. High Energy Phys. 1204, 103 (2012). [arXiv:1203.0015 [hep-th]]

    Google Scholar 

  46. M.R. Gaberdiel, R. Gopakumar, Minimal model holography. J. Phys. A 46, 214002 (2013). [arXiv:1207.6697 [hep-th]]

    Google Scholar 

  47. M. Ammon, M. Gutperle, P. Kraus, E. Perlmutter, Black holes in three dimensional higher spin gravity: a review. J. Phys. A 46, 214001 (2013). [arXiv:1208.5182 [hep-th]]

    Google Scholar 

  48. K. Jin, Higher spin gravity and exact holography. PoS Corfu 2012, 086 (2013). [arXiv:1304.0258 [hep-th]]

    Google Scholar 

  49. B. Chen, J. Long, Y.-n. Wang, Black holes in truncated higher spin AdS3 gravity. J. High Energy Phys. 1212, 052 (2012). [arXiv:1209.6185 [hep-th]]

    Google Scholar 

  50. J.R. David, M. Ferlaino, S.P. Kumar, Thermodynamics of higher spin black holes in 3D. J. High Energy Phys. 1211, 135 (2012). [arXiv:1210.0284 [hep-th]]

    Google Scholar 

  51. B. Chen, J. Long, Y. -N. Wang, “Phase Structure of Higher Spin Black Hole.” JHEP 1303, 017 (2013). [arXiv:1212.6593]

    Article  ADS  MathSciNet  Google Scholar 

  52. P. Kraus, T. Ugajin, An entropy formula for higher spin black holes via conical singularities. J. High Energy Phys. 1305, 160 (2013). [arXiv:1302.1583 [hep-th]]

    Google Scholar 

  53. J. de Boer, J.I. Jottar, Thermodynamics of higher spin black holes in AdS 3. J. High Energy Phys. 1401, 023 (2014). [arXiv:1302.0816 [hep-th]]

    Google Scholar 

  54. J. de Boer, J.I. Jottar, “Entanglement entropy and higher spin holography in AdS3.” (2013). arXiv:1306.4347 [hep-th]

    Google Scholar 

  55. M. Beccaria, G. Macorini, On the partition functions of higher spin black holes. J. High Energy Phys. 1312, 027 (2013). [arXiv:1310.4410 [hep-th]]

    Google Scholar 

  56. M. Beccaria, G. Macorini, “Analysis of higher spin black holes with spin-4 chemical potential.” (2013). arXiv:1312.5599 [hep-th]

    Google Scholar 

  57. B. Chen, J. Long, J. -J. Zhang, “Holographic Rényi entropy for CFT with W symmetry.” arXiv:1312.5510 [hep-th]

    Google Scholar 

  58. S. Datta, J.R. David, M. Ferlaino, S.P. Kumar, Higher spin entanglement entropy from CFT. (2014). arXiv:1402.0007 [hep-th]

    Google Scholar 

  59. M. Henneaux, C. Martínez, R. Troncoso, J. Zanelli, “Black holes and asymptotics of 2 + 1 gravity coupled to a scalar field.” Phys. Rev. D 65, 104007 (2002). [arXiv:hep-th/0201170]

    Article  ADS  MathSciNet  Google Scholar 

  60. M. Henneaux, C. Martínez, R. Troncoso, J. Zanelli, “Asymptotically anti-de Sitter spacetimes and scalar fields with a logarithmic branch. ” Phys. Rev. D 70, 044034 (2004). [hep-th/0404236]

    Article  ADS  MathSciNet  Google Scholar 

  61. R.M. Wald, “Black hole entropy is the noether charge.” Phys. Rev. D 48, 3427 (1993). [gr-qc/9307038]

    Google Scholar 

  62. M. Ammon, A. Castro, N. Iqbal, Wilson lines and entanglement entropy in higher spin gravity. J. High Energy Phys. 1310, 110 (2013). [arXiv:1306.4338 [hep-th]]

    Google Scholar 

  63. L. McGough, H. Verlinde, Bekenstein-Hawking entropy as topological entanglement entropy. J. High Energy Phys. 1311, 208 (2013). [arXiv:1308.2342 [hep-th]]

    Google Scholar 

  64. W. Li, F.-L. Lin, C.-W. Wang, Modular properties of 3D higher spin theory. J. High Energy Phys. 1312, 094 (2013). [arXiv:1308.2959 [hep-th]]

    Google Scholar 

  65. A. Chowdhury, A. Saha, Phase structure of higher spin black holes (2013). arXiv:1312.7017 [hep-th]

    Google Scholar 

  66. M. Gutperle, E. Hijano, J. Samani, Lifshitz black holes in higher spin gravity (2013). arXiv:1310.0837 [hep-th]

    Google Scholar 

  67. A.M. Polyakov, Gauge transformations and diffeomorphisms. Int. J. Mod. Phys. A 5, 833 (1990).

    Article  ADS  MathSciNet  Google Scholar 

  68. M. Bershadsky, “Conformal field theories via Hamiltonian reduction. ”Commun. Math. Phys. 139, 71 (1991)

    Google Scholar 

  69. I. Fujisawa, R. Nakayama, “Second-order formalism for 3D spin-3 gravity.”Class. Quant. Gravity 30, 035003 (2013). [arXiv:1209.0894 [hep-th]]

    Google Scholar 

  70. A. Campoleoni, S. Fredenhagen, S. Pfenninger, Asymptotic W-symmetries in three-dimensional higher-spin gauge theories. ” J. High Energy Phys. 1109, 113 (2011). [arXiv:1107.0290 [hep-th]]

    Google Scholar 

  71. M.R. Gaberdiel, T. Hartman, Symmetries of holographic minimal models. J. High Energy Phys. 1105, 031 (2011). [arXiv:1101.2910 [hep-th]]

    Google Scholar 

  72. P. Kraus, E. Perlmutter, “Partition functions of higher spin black holes and their CFT duals. ”J. High Energy Phys. 1111, 061 (2011). [arXiv:1108.2567 [hep-th]]

    Google Scholar 

  73. H.-S. Tan, “Aspects of three-dimensional spin-4 gravity.” J. High Energy Phys. 1202, 035 (2012). [arXiv:1111.2834 [hep-th]]

    Google Scholar 

  74. M. Gary, D. Grumiller, R. Rashkov, “Towards non-AdS holography in 3-dimensional higher spin gravity.” J. High Energy Phys. 1203, 022 (2012). [arXiv:1201.0013 [hep-th]]

    Google Scholar 

  75. M. Banados, R. Canto, S. Theisen, “The action for higher spin black holes in three dimensions.”J. High Energy Phys. 1207, 147 (2012). [arXiv:1204.5105 [hep-th]]

    Google Scholar 

  76. M. Ferlaino, T. Hollowood, S.P. Kumar, “Asymptotic symmetries and thermodynamics of higher spin black holes in AdS3,” Phys. Rev. D 88, 066010 (2013). [arXiv:1305.2011 [hep-th]]

    Google Scholar 

  77. M. Henneaux, G. Lucena Gómez, J. Park, S.-J. Rey, “Super- W(infinity) asymptotic symmetry of higher-spin AdS 3 supergravity.” J. High Energy Phys. 1206, 037 (2012). [arXiv:1203.5152 [hep-th]]

    Google Scholar 

  78. B. Chen, J. Long, Y. -N. Wang, “Conical Defects, Black Holes and Higher Spin (Super-) Symmetry.” JHEP 1306, 025 (2013). [arXiv:1303.0109 [hep-th]]

    Google Scholar 

  79. S. Datta, J.R. David, Black holes in higher spin supergravity. J. High Energy Phys. 1307, 110 (2013). [arXiv:1303.1946 [hep-th]]

    Google Scholar 

  80. H.S. Tan, “Exploring three-dimensional higher-spin supergravity based on sl(N \(\vert\) N - 1) Chern-Simons theories.” J. High Energy Phys. 1211, 063 (2012). [arXiv:1208.2277 [hep-th]]

    Google Scholar 

  81. M.R. Gaberdiel, R. Gopakumar, A. Saha, “Quantum W-symmetry in AdS 3,” J. High Energy Phys. 1102, 004 (2011). [arXiv:1009.6087 [hep-th]]

    Google Scholar 

  82. M.R. Gaberdiel, R. Gopakumar, “An AdS 3 dual for minimal model CFTs.” Phys. Rev. D 83, 066007 (2011). [arXiv:1011.2986 [hep-th]]

    Google Scholar 

  83. M.R. Gaberdiel, R. Gopakumar, T. Hartman, S. Raju, “Partition functions of holographic minimal models.” J. High Energy Phys. 1108, 077 (2011). [arXiv:1106.1897 [hep-th]]

    Google Scholar 

  84. A. Castro, R. Gopakumar, M. Gutperle, J. Raeymaekers, Conical defects in higher spin theories. J. High Energy Phys. 1202, 096 (2012). [arXiv:1111.3381 [hep-th]]

    Google Scholar 

  85. M. Ammon, P. Kraus, E. Perlmutter, “Scalar fields and three-point functions in D = 3 higher spin gravity. ” J. High Energy Phys. 1207, 113 (2012). [arXiv:1111.3926 [hep-th]]

    Google Scholar 

  86. M.R. Gaberdiel, P. Suchanek, “Limits of minimal models and continuous orbifolds. ” J. High Energy Phys. 1203, 104 (2012). [arXiv:1112.1708 [hep-th]]

    Google Scholar 

  87. P. Kraus, E. Perlmutter, Probing higher spin black holes. J. High Energy Phys. 1302, 096 (2013). [arXiv:1209.4937 [hep-th]]

    Google Scholar 

  88. S. Banerjee, A. Castro, S. Hellerman, E. Hijano, A. Lepage-Jutier, A. Maloney, S. Shenker, “Smoothed transitions in higher spin AdS gravity.”Class. Quant. Grav. 30, 104001 (2013). [arXiv:1209.5396 [hep-th]]

    Google Scholar 

  89. A. Campoleoni, T. Prochazka, J. Raeymaekers, A note on conical solutions in 3D Vasiliev theory. J. High Energy Phys. 1305, 052 (2013). [arXiv:1303.0880 [hep-th]]

    Google Scholar 

  90. M.R. Gaberdiel, K. Jin, E. Perlmutter, “Probing higher spin black holes from CFT. ” J. High Energy Phys. 1310, 045 (2013). [arXiv:1307.2221 [hep-th]]

    Google Scholar 

  91. A. Campoleoni, S. Fredenhagen, On the higher-spin charges of conical defects. Phys. Lett. B 726, 387 (2013). [arXiv:1307.3745]

    Article  ADS  Google Scholar 

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Acknowledgements

We thank G. Barnich, X. Bekaert, E. Bergshoeff, C. Bunster, A. Campoleoni, R. Canto, D. Grumiller, M. Henneaux, J. Jottar, C. Martínez, J. Matulich, J. Ovalle, R. Rahman, S-J Rey, J. Rosseel, C. Troessaert and M. Vasiliev for stimulating discussions. R.T. also thanks E. Papantonopoulos and the organizers of the Seventh Aegean Summer School, “Beyond Einstein’s theory of gravity”, for the opportunity to give this lecture in a wonderful atmosphere. This work is partially funded by the Fondecyt grants N∘ 1130658, 1121031, 11130260, 11130262. The Centro de Estudios Científicos (CECs) is funded by the Chilean Government through the Centers of Excellence Base Financing Program of Conicyt.

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  1. Centro de Estudios Científicos (CECs), Casilla, 1469, Valdivia, Chile

    Alfredo Pérez, David Tempo & Ricardo Troncoso

  2. Universidad Andrés Bello, Av. Repblica 440, Santiago, Chile

    Ricardo Troncoso

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  1. Alfredo Pérez
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Correspondence to Ricardo Troncoso .

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  1. Department of Physics, National Technical University of Athens, Athens, Greece

    Eleftherios Papantonopoulos

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Pérez, A., Tempo, D., Troncoso, R. (2015). Higher Spin Black Holes. In: Papantonopoulos, E. (eds) Modifications of Einstein's Theory of Gravity at Large Distances. Lecture Notes in Physics, vol 892. Springer, Cham. https://doi.org/10.1007/978-3-319-10070-8_10

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