# The (2 + 1)-dimensional black hole

@article{Carlip1995The, title={The (2 + 1)-dimensional black hole}, author={Steven Carlip}, journal={Classical and Quantum Gravity}, year={1995}, volume={12}, pages={2853-2880} }

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 shares many of the characteristics of the Kerr black hole: it has an event horizon, an inner horizon, and an ergosphere; it occurs as an endpoint of gravitational collapse; it exhibits mass inflation; and it has a non-vanishing Hawking temperature and interesting thermodynamic properties. At the same…

## 327 Citations

Dynamical Black Holes in 2+1 Dimensions

- Physics
- 2013

We investigate the global structure of a recently discovered simple exact, non-stationary solution of topologically massive and new massive gravity with the asymptotic charges of an undeformed BTZ…

Asymptotic charged BTZ black hole solutions

- Physics
- 2012

The well-known (2 + 1)-dimensional Reissner-Nordström (BTZ) black hole can be generalized to three dimensional Einstein-nonlinear electromagnetic field, motivated from obtaining a finite value for…

The First Law of Thermodynamics of the (2+1)-Dimensional Banados--Teitelboim--Zanelli Black Holes and Kerr--de Sitter Spacetimes

- Physics
- 2006

We investigate the first law of thermodynamics in the case of the (2+1)-dimensional Banados–Teitelboim–Zanelli black holes and Kerr–de Sitter spacetimes. In particular, we focus on the integral mass…

Hawking radiation from covariant anomalies in (2+1)-dimensional black holes

- Physics
- 2009

In an insightful approach, Robinson and Wilczek proposed that Hawking radiation can be obtained as the compensation of a breakdown of general covariance and gauge invariance and the radiation is a…

Classical and quantum analysis of an Einstein-Scalar solution in 2 + 1 dimensions

- Physics
- 2017

Abstract.The classical and quantum properties of a new solution obtained in (2 + 1) -dimensional gravity coupled with a real scalar field is analyzed in detail. The considered new solution is a…

Conformal field theory, (2 + 1)-dimensional gravity and the BTZ black hole

- Physics
- 2005

In three spacetime dimensions, general relativity becomes a topological field theory, whose dynamics can be largely described holographically by a two-dimensional conformal field theory at the…

A New Class of Stable (2+1) Dimensional Thin Shell Wormhole

- Physics
- 2011

Few years ago, Bañados, Teitelboim and Zanelli (BTZ) (in Phys. Rev. Lett. 69:1849 (1992)) has discovered an explicit vacuum solution of (2+1)-dimensional gravity with negative cosmological constant.…

The off-shell black hole

- Physics
- 1995

The standard (Euclidean) action principle for the gravitational field implies that for spacetimes with black-hole topology, the opening angle at the horizon and the horizon area are canonical…

Geometrical and hydrodynamic aspects of five-dimensional Schwarzschild black hole

- Physics
- 2014

Exploiting the five-dimensional Schwarzschild black hole, we study the geometrical natures of higher-dimensional black holes to yield the (6+1)-dimensional global embedding Minkowski space structure.…

Negative spectrum of the 2 + 1 black hole

- Physics
- 2009

In (2+1)-dimensional gravity with negative cosmological constant, the states in the negative energy range, between anti-de Sitter (AdS) (M=-1) and the so-called Banados-Teitelboim-Zanelli black hole…

## References

SHOWING 1-10 OF 92 REFERENCES

Gauge formulation of the spinning black hole in (2+1)-dimensional anti-de Sitter space.

- Physics, MedicinePhysical review. D, Particles and fields
- 1993

We compute the group element of SO(2,2) associated with the spinning black hole found by Ba\~nados, Teitelboim, and Zanelli in (2+1)-dimensional anti-de Sitter space-time. We show that their metric…

Black hole in three-dimensional spacetime.

- Physics, MedicinePhysical review letters
- 1992

The standard Einstein-Maxwell equations in 2+1 spacetime dimensions, with a negative cosmological constant, admit a black hole solution that appears as a negative energy state separated by a mass gap from the continuous black hole spectrum.

Supersymmetry of the (2+1)-dimensional black holes.

- Physics, MedicinePhysical review letters
- 1994

It is argued that the zero-mass hole is the ground state of (1,1) adS supergravity with periodic (``Ramond'') boundary conditions on the spinor fields.

Aspects of black hole quantum mechanics and thermodynamics in 2+1 dimensions.

- Physics, MedicinePhysical review. D, Particles and fields
- 1995

It is shown that the dynamical variables of the black hole arise from the possibility of a deficit angle at the (Euclidean) horizon, and briefly speculate as to how they may provide a basis for a statistical picture of black hole thermodynamics.

Black holes in three-dimensional topological gravity.

- Physics, MedicinePhysical review. D, Particles and fields
- 1995

It is found that the theory with topological matter reverses the identification of energy and angular momentum with the parameters in the metric, compared with general relativity, and that the entropy is determined by the circumference of the inner rather than the outer horizon.

Geodesic structure of the (2 + 1)-dimensional BTZ black hole

- Physics
- 1994

Null and time-like geodesics around a 2+1 black hole are determined. Complete geodesics of both types exist in the rotating black-hole background, but not in the spinless case. Upper and lower bounds…

Horizon quantization and thermodynamics of the 2+1 black hole

- Physics
- 1994

We test on the 2+1 dimensional black hole the quantization method that we have previously proposed in four dimensions. While in the latter case the horizon dynamics is described, at the effective…

Hawking radiation of Dirac fields in the (2+1)-dimensional black hole space-time.

- Physics, MedicinePhysical review. D, Particles and fields
- 1995

By calculating the response function, we study the Hawking radiation of massless Dirac fields in the (2+1)-dimensional black hole geometry. We find that the response function has Planck…

Lectures in (2+1)-Dimensional Gravity

- Physics
- 1995

These lectures briefly review our current understanding of classical and quantum gravity in three spacetime dimensions, concentrating on the quantum mechanics of closed universes and the…

Geometry of the 2+1 black hole.

- Physics, MedicinePhysical review. D, Particles and fields
- 1993

The geometry of the spinning black holes of standard Einstein theory in 2+1 dimensions, with a negative cosmological constant, and without couplings to matter, is analyzed in detail. It is shown that…