The thermodynamics of self-gravitating systems in equilibrium is holographic

Abstract

We show that, when we study the coexistence of the general relativity with thermodynamics, some physical properties that are usually thought of as holographic and lying in the domain of quantum gravity can actually be accessed even at the classical level. In particular, we demonstrate that the thermodynamics of the gravitating systems in equilibrium is fully specified by the variables defined on the system’s boundary, namely, the boundary’s geometry and extrinsic curvature. Hence, information is non-trivially incorporated in boundary variables because of the structure (the symmetries) of the classical gravity theory, without any input from the quantum theory (such as black hole entropy).