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In three spacetime dimensions, general relativity drastically simplifies, becoming a "topological" theory with no propagating local degrees of freedom. Nevertheless, many of the difficult conceptual problems of quantizing gravity are still present. In this review, I summarize the rather large body of work that has gone towards quantizing (2 + 1)-dimensional… (More)

- S Carlip
- 1999

On a manifold with boundary, the constraint algebra of general relativity may acquire a central extension, which can be computed using covariant phase space techniques. When the boundary is a (local) Killing horizon, a natural set of boundary conditions leads to a Virasoro subalgebra with a calculable central charge. Conformal field theory methods may then… (More)

- S Carlip
- 1998

When restricted to the horizon of a black hole, the " gauge " algebra of surface deformations in general relativity contains a physically important Virasoro subalgebra with a calculable central charge. The fields in any quantum theory of gravity must transform under this algebra; that is, they must admit a conformal field theory description. With the aid of… (More)

- Steven Carlip, Claudio Teitelboim
- 1994

We discuss the quantum mechanics and thermodynamics of the (2+1)-dimensional black hole, using both minisuperspace methods and exact results from Chern-Simons theory. In particular, we evaluate the first quantum correction to the black hole entropy. We show that the dynamical variables of the black hole arise from the possibility of a deficit angle at the… (More)

- S Carlip
- 1995

I review the classical and quantum properties of the (2+1)-dimensional black hole of Bañados, Teitelboim, and Zanelli. This solution of the Einstein field equations in three space-time 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… (More)

- S Carlip
- 1998

With the recent discovery that many aspects of black hole thermodynamics can be effectively reduced to problems in three spacetime dimensions, it has become increasingly important to understand the " statistical mechanics " of the (2+1)-dimensional black hole of Bañados, Teitelboim, and Zanelli (BTZ). Several conformal field theoretic derivations of the BTZ… (More)

- S Carlip
- 1994

The presence of a horizon breaks the gauge invariance of (2+1)-dimensional general relativity, leading to the appearance of new physical states at the horizon. I show that the entropy of the (2+1)-dimensional black hole can be obtained as the logarithm of the number of these microscopic states.

Near an event horizon, the action of general relativity acquires a new asymptotic conformal symmetry. For two-dimensional dilaton gravity, this symmetry results in a chiral Virasoro algebra, and Cardy's formula for the density of states reproduces the Bekenstein-Hawking entropy. This lends support to the notion that black hole entropy is controlled… (More)

- S Carlip
- 2008

Three-dimensional topologically massive AdS gravity has a complicated constraint algebra, making it difficult to count nonperturbative degrees of freedom. I show that a new choice of variables greatly simplifies this algebra, and confirm that the theory contains a single propagating mode for all values of the mass parameter and the cosmological constant. As… (More)

- S Carlip
- 1999

String theory and " quantum geometry " have recently offered independent statistical mechanical explanations of black hole thermodynamics. But these successes raise a new problem: why should models with such different microscopic degrees of freedom yield identical results? I propose that the asymptotic behavior of the density of states at a black hole… (More)