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

@article{Carlip2005ConformalFT, title={Conformal field theory, (2 + 1)-dimensional gravity and the BTZ black hole}, author={Steven Carlip}, journal={Classical and Quantum Gravity}, year={2005}, volume={22} }

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 'boundary' of spacetime. I review what is known about this reduction—mainly within the context of pure (2 + 1)-dimensional gravity—and discuss its implications for our understanding of the statistical mechanics and quantum mechanics of black holes.

## 163 Citations

Conformal field theory on the horizon of a BTZ black hole

- PhysicsChinese Physics C
- 2018

In a three-dimensional spacetime with negative cosmological constant, general relativity can be written as two copies of SO(2,1) Chern-Simons theory. On a manifold with a boundary, the Chern-Simons…

Four-Dimensional Entropy from Three-Dimensional Gravity.

- Physics, MedicinePhysical review letters
- 2015

It is shown how to use this correspondence to obtain the entropy of the (3+1)-dimensional black hole from well-understood conformal field theory computations of the entropy in (2+1-dimensional de Sitter space.

The BTZ black hole as a Lorentz-flat geometry

- Physics
- 2014

Abstract It is shown that 2 + 1 dimensional anti-de Sitter spacetimes are Lorentz-flat. This means, in particular, that any simply-connected patch of the BTZ black hole solution can be endowed with a…

Horizon mechanics and asymptotic symmetries with an Immirzi-like parameter in 2 + 1 dimensions

- Physics
- 2011

Starting with a generalized theory of 2 + 1 gravity containing an Immirzi-like parameter, we derive the modified laws of black hole mechanics using the formalism of weak isolated horizons.…

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…

An sl(2,R) current algebra from AdS 3 gravity

- Physics
- 2013

We provide a set of chiral boundary conditions for three-dimensional gravity that allow for asymptotic symmetries identical to those of two-dimensional induced gravity in light-cone gauge considered…

Covariant description of the black hole entropy in 3D gravity

- Physics
- 2007

We study the entropy of the black hole with torsion using the covariant form of the partition function. The regularization of infinities appearing in the semiclassical calculation is shown to be…

New massive gravity and AdS(4) counterterms.

- Physics, MedicinePhysical review letters
- 2011

This theory is rewritten in terms of the gauge field that is used to recast 3D gravity as a Chern-Simons theory and the parameter values of the resulting counterterm action correspond to a c=0 theory in the context of the duality between AdS(3) gravity and two-dimensional conformal field theory.

Eigenvalue Problem of Scalar Fields in BTZ Black Hole Spacetime

- Physics
- 2008

We studied the eigenvalue problem of scalar fields in the (2+1)-dimensional BTZ black hole spacetime. The Dirichlet boundary condition at infinity and the Dirichlet or the Neumann boundary condition…

Conformal boundary conditions, loop gravity and the continuum

- PhysicsJournal of High Energy Physics
- 2018

A bstractIn this paper, we will make an attempt to clarify the relation between three-dimensional euclidean loop quantum gravity with vanishing cosmological constant and quantum field theory in the…

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