We consider string theory in the background of the two-dimensional black hole as described by the SL(2, R)/U(1) coset theory recently introduced by Witten. We study the spectrum of this conformal field theory, and give explicit representations for the tachyon vertex operators in terms of SL(2, R) matrix elements. This is used to compute the scattering of strings off the black hole and to show t...

Abstract The Hessian of the entropy function can be thought of as a metric tensor on state space. In the context of thermodynamical fluctuation theory Ruppeiner has argued that the Riemannian geometry of this metric gives insight into the underlying statistical mechanical system; the claim is supported by numerous examples. We study these geometries for some families of black holes and find tha...

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 the black hole arises from identifications of points of anti-de Sitter space by a discrete subgroup of SO(2, 2). The generic black hole is a smooth manifold in the metric sense. The surface r = 0 is...

A ‘black hole sector’ of non-perturbative canonical quantum gravity is introduced. The quantum black hole degrees of freedom are shown to be described by a Chern-Simons field theory on the horizon. It is shown that the entropy of a large non-rotating black hole is proportional to its horizon area. The constant of proportionality depends upon the Immirzi parameter, which fixes the spectrum of th...

The geometric operators of area, volume, and length, depend on a fundamental length l of quantum geometry which is a priori arbitrary rather than equal to the Planck length lP . The fundamental length l and the Immirzi parameter γ determine each other. With any l the entropy formula is rendered most naturally in units of the length gap √ 3/2( √ γl). Independently of the choice of l, the black h...

We examine the linear stability of various configurations in Bose-Einstein condensates with sonic horizons. These configurations are chosen in analogy with gravitational systems with a black hole horizon, a white hole horizon and a combination of both. We discuss the role of different boundary conditions in this stability analysis, paying special attention to their meaning in gravitational term...