The entropy of a hole in spacetime

TL;DR

This paper calculates the gravitational entropy of a spherical Rindler space, showing it equals a quarter of the horizon area and proposing it as entanglement entropy between interior and exterior quantum gravitational degrees of freedom.

Contribution

It introduces a new calculation of gravitational entropy for a time-dependent spherical Rindler space and links it to entanglement entropy in quantum gravity.

Findings

Entropy equals A/4G, with A as the horizon area.

The horizon coincides with the boundary of the spherical region.

Proposes entanglement interpretation of the entropy.

Abstract

We compute the gravitational entropy of 'spherical Rindler space', a time-dependent, 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 = A/4G, where 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.