Dynamics of diffeomorphism degrees of freedom at a horizon

Abstract

We define a set of boundary conditions that ensure the presence of a null hypersurface with the essential characteristics of a horizon, using the formalism of weakly isolated horizons as a guide. We then determine the diffeomorphisms that preserve these boundary conditions, and derive a dynamical action for these diffeomorphisms in a neighborhood of the horizon. The action is similar to that of the Liouville theory, and the equation of motion of the gravitational degrees of freedom approaches that of a free two-dimensional conformal field in the near-horizon region.