Raychaudhuri Equation, Geometrical Flows and Geometrical Entropy

Abstract

The Raychaudhuri equation is derived by assuming geometric flow in space–time M of n+1 dimensions. The equation turns into a harmonic oscillator form under suitable transformations. Thereby, a relation between geometrical entropy and mean geodesic deviation is established. This has a connection to chaos theory where the trajectories diverge exponentially. We discuss its application to cosmology and black holes. Thus, we establish a connection between chaos theory and general relativity.