Stochastic congruence equations for spacetime fluctuations

Abstract

This work considers some implications of viewing gravity as an emergent force. In such a viewpoint, general relativity arises as the thermodynamic limit of some microscopic theory. As such, one would expect the macroscopic variables such as the curvature tensors to fluctuate about their mean. This thesis presents a method for analyzing the effects of curvature fluctuations on spacetime thermodynamics. This is done by examining the evolution equations for time-like and null congruences, and recasting them as stochastic differential equations. The purpose of viewing the congruence evolution equations as stochastic is in the spirit of nonequilibrium thermodynamics, and may lead to an application of the fluctuation-dissipation theorem to spacetime. It is expected that this reformulation of the congruence equations will lead to further insights on the effects of fluctuations in general relativity.