Thermodynamic properties of causal horizons - Barbosa, Matheus Goulart (2020)
Black hole thermodynamics emerged as a surprising connection between thermodynamics and general relativity, showing that one may attribute properties like entropy and temperature to a black hole´s event horizon. Inspired by it, studies from the last decades indicate that this analogy extends itself to many models and systems in which one considers the existence of causal horizons. Given certain assumptions, it is even possible to derive Einstein´s field equations from the laws of thermodynamics. Nevertheless, this result was not constructed on foundations so solid as those of black hole thermodynamics, leaving room for a formalization of these ideas. Therefore, in order to advance in the generalization of the relation between thermodynamics and gravitation, one may focus on the study of the geometry of causal horizons, which correspond to lightlike hypersurfaces of a spacetime. In this work, we review the laws of black hole thermodynamics, giving special attention to the generalized second law, and show how the mentioned analogy is formulated for general causal horizons. Then, we present the induced geometric objects on lightlike hypersurfaces, providing the basic mathematical tools to analyze the geometry of causal horizons.