Steven Carlip

Learn 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)
Restricted to a black hole horizon, the “gauge” algebra of surface deformations in general relativity contains a Virasoro subalgebra with a calculable central charge. The fields in any quantum theory of gravity must transform accordingly, i.e., they must admit a conformal field theory description. Applying Cardy’s formula for the asymptotic density of(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 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(More)
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)
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)
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)
For simple enough spatial topologies, at least four approaches to (2 + 1)-dimensional quantum gravity have been proposed: Wheeler-DeWitt quantization, canonical quantization in Arnowitt-Deser-Misner (ADM) variables on reduced phase space, Chern-Simons quantization, and quantization in terms of Ashtekar-Rovelli-Smolin loop variables. An important problem is(More)
The problem of reconciling general relativity and quantum theory has fascinated and bedeviled physicists for more than 70 years. Despite recent progress in string theory and loop quantum gravity, a complete solution remains out of reach. I review the status of the continuing effort to quantize gravity, emphasizing the underlying conceptual issues and the(More)