nLab BTZ black hole




black holes in 3d gravity with negative cosmological constant


Euclidean BTZ is hyperbolic solid torus

The Euclidean BTZ black hole is a hyperbolic 3-manifold homeomorphic to (the interior of) the hyperbolic solid torus, hence to the knot complement of the unknot in the 3-sphere.

(e.g Gukov 03, appendix A, Kraus 06, around Fig. 1, BKR 07, 2.1)

Notice that the volume of the hyperbolic solid torus is not finite. Therefore this hyperbolic 3-manifold knot complement does not count as a “knot complement with hyperbolic structure” in the sense of Thurston‘s classification of 3-manifolds? (see also this MO discussion).



The original BTZ black hole with trivial internal topology is due to:

The generalization to arbitrary black holes in 2+1-dimensional AdS gravity, with generally non-trivial internal topology:

  • Stefan Aminneborg, Ingemar Bengtsson, Dieter Brill, Soren Holst, Peter Peldan, Black Holes and Wormholes in 2+1 Dimensions, Class. Quant. Grav. 15 (1998) 627-644 (arXiv:gr-qc/9707036)

  • Stefan Aminneborg, Ingemar Bengtsson, Soren Holst, A Spinning Anti-de Sitter Wormhole, Class. Quant. Grav. 16 (1999) 363-382 (arXiv:gr-qc/9805028)

  • Dieter Brill, Black Holes and Wormholes in 2+1 Dimensions, In: Cotsakis S., Gibbons G.W. (eds) Mathematical and Quantum Aspects of Relativity and Cosmology. Lecture Notes in Physics, vol 537. Springer, Berlin, Heidelberg (arXiv:gr-qc/9904083, doi:10.1007/3-540-46671-1_6 )

See also:

  • Aritra Ghosh, Chandrasekhar Bhamidipati, Thermodynamic geometry and interacting microstructures of BTZ black holes (arXiv:2001.10510)

  • Roberto Emparan, Antonia Micol Frassino, Benson Way, Quantum BTZ black hole, JHEP11 (2020) 137 (arXiv:2007.15999)

  • Pablo Bueno, Pablo A. Cano, Javier Moreno, Guido van der Velde, Regular black holes in three dimensions (arXiv:2104.10172)

  • Matías Briceño, Cristián Martínez, Jorge Zanelli, On the central singularity of the BTZ geometries [arXiv:2404.06552]

In view of the cosmic censorship hypothesis:

Via topological M-theory:

  • Javier Chagoya, Graciela Reyes-Ahumada, M. Sabido, BTZ entropy from topological M-theory (arXiv:2011.01094)

See also:

Euclidean BTZ black holes

Discussion of Euclidean BTZ black holes/thermal AdS3 (the hyperbolic solid torus), partly with an eye towards black hole entropy computed via AdS3/CFT2:

See also:

  • Zhen-Ming Xu, Bin Wu, Wen-Li Yang, Thermodynamic curvature and isoperimetric inequality for the charged BTZ black hole (arXiv:2002.00117)

    (not Euclidean, but thermodynamic)

Wilson lines computing holographic entropy in AdS 3/CFT 2AdS_3/CFT_2

Discussion of BTZ black hole entropy and more generally of holographic entanglement entropy in 3d quantum gravity/AdS3/CFT2 via Wilson line observables in Chern-Simons theory:

  • Martin Ammon, Alejandra Castro, Nabil Iqbal, Wilson Lines and Entanglement Entropy in Higher Spin Gravity, JHEP 10 (2013) 110 (arXiv:1306.4338)

  • Jan de Boer, Juan I. Jottar, Entanglement Entropy and Higher Spin Holography in AdS 3AdS_3, JHEP 1404:089, 2014 (arXiv:1306.4347)

  • Alejandra Castro, Stephane Detournay, Nabil Iqbal, Eric Perlmutter, Holographic entanglement entropy and gravitational anomalies, JHEP 07 (2014) 114 (arXiv:1405.2792)

  • Mert Besken, Ashwin Hegde, Eliot Hijano, Per Kraus, Holographic conformal blocks from interacting Wilson lines, JHEP 08 (2016) 099 (arXiv:1603.07317)

  • Andreas Blommaert, Thomas G. Mertens, Henri Verschelde, The Schwarzian Theory - A Wilson Line Perspective, JHEP 1812 (2018) 022 (arXiv:1806.07765)

  • Ashwin Dushyantha Hegde, Role of Wilson Lines in 3D Quantum Gravity, 2019 (spire:1763572)

  • Xing Huang, Chen-Te Ma, Hongfei Shu, Quantum Correction of the Wilson Line and Entanglement Entropy in the AdS 3AdS_3 Chern-Simons Gravity Theory (arXiv:1911.03841)

  • Eric D'Hoker, Per Kraus, Gravitational Wilson lines in AdS 3AdS_3 (arXiv:1912.02750)

  • Marc Henneaux, Wout Merbis, Arash Ranjbar, Asymptotic dynamics of AdS 3AdS_3 gravity with two asymptotic regions (arXiv:1912.09465)

and similarly for 3d flat-space holography:

Discussion for 3d de Sitter spacetime:

  • Alejandra Castro, Philippe Sabella-Garnier, Claire Zukowski, Gravitational Wilson Lines in 3D de Sitter (arXiv:2001.09998)

In pp-adic AdS/CFT

Discussion of BTZ black holes via tensor networks in the p-adic AdS/CFT correspondence:

Last revised on April 11, 2024 at 03:19:23. See the history of this page for a list of all contributions to it.