Black hole in three-dimensional spacetime.

  title={Black hole in three-dimensional spacetime.},
  author={Ba{\~n}ados and Teitel'boim and Zanelli},
  journal={Physical review letters},
  volume={69 13},
The standard Einstein-Maxwell equations in 2+1 spacetime dimensions, with a negative cosmological constant, admit a black hole solution. The 2+1 black hole---characterized by mass, angular momentum, and charge, defined by flux integrals at infinity---is quite similar to its 3+1 counterpart. Anti--de Sitter space appears as a negative energy state separated by a mass gap from the continuous black hole spectrum. Evaluation of the partition function yields that the entropy is equal to twice the… 

2 + 1‐dimensional black holes with momentum and angular momentum

Exact solutions of Einstein's equations in 2 + 1‐dimensional anti‐de Sitter space containing any number of black holes are described. In addition to the black holes these spacetimes can possess

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2 + 1 black hole with a dynamical conical singularity

We find black hole solutions to Euclidean 2 + 1 gravity coupled to a relativistic particle which have a dynamical conical singularity at the horizon. These solutions mimic the tree level contribution

Scale-dependent three-dimensional charged black holes in linear and non-linear electrodynamics

In the present work we study the scale dependence at the level of the effective action of charged black holes in Einstein–Maxwell as well as in Einstein–power-Maxwell theories in

The (2 + 1)-dimensional black hole

I review the classical and quantum properties of the (2 + 1)-dimensional black hole of Banados, Teitelboim and Zanelli. This solution of the Einstein field equations in three spacetime dimensions



Lower-dimensional gravity.

  • Verbin
  • Physics, Medicine
    Physical review. D, Particles and fields
  • 1994


  • Quantum Grav. 10: L54
  • 1993

This makes the metric complex when J = 0. The Euclidean action is given by iI = −I Euc . Although correct in the case at hand, making imaginary a particular coordinate in a generally covariant theory

    We thank E.Witten for pointing this out to us

      Ann. Phy

      • Ann. Phy
      • 1984

      That canonical conjugates in the sense of classical mechanics become thermodynamical conjugates has been noticed by

      • Class

      That the entropy may be written as a surface term on the horizon has been observed previously by

      • Phy. Rev. Lett
      • 1990

      Electronic address: cecsnet@uchcecvm.bitnet

        Phy. Rev. D

        • Phy. Rev. D
        • 1977