The entropy of a hole in spacetime

Abstract

Abstract We compute the gravitational entropy of “spherical Rindler space”, a timedependent, spherically symmetric generalization of ordinary Rindler space, defined with reference to a family of observers traveling along non-parallel, accelerated trajectories. All these observers are causally disconnected from a spherical region H (a “hole”) located at the origin of Minkowski space. The entropy evaluates to S = $ \mathcal{A} $ /4G, where $ \mathcal{A} $ is the area of the spherical acceleration horizon, which coincides with the boundary of H. We propose that S is the entropy of entanglement between quantum gravitational degrees of freedom supporting the interior and the exterior of the sphere H.