nLab BTZ black hole

Idea

black holes in 3d gravity with negative cosmological constant

Properties

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).

Related concepts

• AdS3/CFT2

References

General

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

• Máximo Bañados, Claudio Teitelboim, Jorge Zanelli, The Black Hole in Three Dimensional Space Time, Phys. Rev. Lett. 69 (1992) 1849-1851 (arXiv:hep-th/9204099)

• Máximo Bañados, Marc Henneaux, Claudio Teitelboim, Jorge Zanelli,

  Geometry of the 2+1 Black Hole, Phys. Rev. D48: 1506-1525, 1993 (arXiv:gr-qc/9302012)

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:

• Roberto Emparan, Marija Tomašević, Strong cosmic censorship in the BTZ black hole, JHEP 06 (2020) 038 (arXiv:2002.02083)

Via topological M-theory:

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

See also:

• Wikipedia, BTZ black hole

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:

• Kirill Krasnov, Holography and Riemann Surfaces, Adv. Theor. Math. Phys. 4 (2000) 929-979 (arXiv:hep-th/0005106)

• Kirill Krasnov, around Figure 6 of: Analytic Continuation for Asymptotically AdS 3D Gravity, Class. Quant. Grav. 19 (2002) 2399-2424 (arXiv:gr-qc/0111049)

• Kirill Krasnov, Black Hole Thermodynamics and Riemann Surfaces, Class. Quant. Grav. 20 (2003) 2235-2250 (arXiv:gr-qc/0302073)

• Sergei Gukov, Appendix A of: Three-Dimensional Quantum Gravity, Chern-Simons Theory, and the A-Polynomial, Commun. Math. Phys. 255: 577-627, 2005 (arXiv:hep-th/0306165)

• Per Kraus, Lectures on black holes and the $AdS_3/CFT_2$ correspondence, Lect. Notes Phys. 755: 193-247, 2008 (arXiv:hep-th/0609074)

• Micha Berkooz, Zohar Komargodski, Dori Reichmann, Thermal $AdS_3$, BTZ and competing winding modes condensation, JHEP 0712:020, 2007 (arXiv:0706.0610)

• M. Cadoni, M. Melis, Holographic entanglement entropy of the BTZ black hole, Found. Phys. 40: 638-657, 2010 (arXiv:0907.1559)

  (relation to holographic entanglement entropy)

• Ingmar Saberi, around Figure 4.3 of: Knots, Trees, and Fields: Common Ground Between Physics and Mathematics (doi:10.7907/Z9VX0DHZ, pdf)

  (with generalization to p-adic string theory)

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 $AdS_3/CFT_2$

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 $AdS_3$, 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 $AdS_3$ Chern-Simons Gravity Theory (arXiv:1911.03841)

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

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

and similarly for 3d flat-space holography:

• Arjun Bagchi, Rudranil Basu, Daniel Grumiller, Max Riegler, Entanglement entropy in Galilean conformal field theories and flat holography, Phys. Rev. Lett. 114, 111602 (2015) (arXiv 1410.4089)

• Rudranil Basu, Max Riegler, Wilson Lines and Holographic Entanglement Entropy in Galilean Conformal Field Theories, Phys. Rev. D 93, 045003 (2016) (arXiv:1511.08662)

• Wout Merbis, Max Riegler, Geometric actions and flat space holography (arXiv:1912.08207)

Discussion for 3d de Sitter spacetime:

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

In $p$-adic AdS/CFT

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

• Matthew Heydeman, Matilde Marcolli, Sarthak Parikh, Ingmar Saberi, Nonarchimedean Holographic Entropy from Networks of Perfect Tensors (arXiv:1812.04057)

• Stephen Ebert, Hao-Yu Sun, Meng-Yang Zhang, Probing holography in $p$-adic CFT (arXiv:1911.06313)