Statistical thermodynamics of a black hole in terms of surface fields

An action principle for spacetimes with the topology of a Euclidean black hole is given. The gravitational field is described by the ordinary volume degrees of freedom plus additional surface fields at the horizon. The surface degrees of freedom correspond to diffeomorphisms on the sphere at the horizon and a field of "opening angles." General covariance forces the surface modes to be confined to a box of an unusual exponential shape, whose volume must be specified as part of the definition of the statistical ensemble. This gives rise to the Bekenstein-Hawking entropy.