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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)
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)
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)
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)
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)
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)
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)