Raychaudhuri Equation, Geometrical Flows and Geometrical Entropy

Lawrence Paul Horwitz, Vishnu S Namboothiri, Gautham Varma K, Asher Yahalom, Yosef Strauss, Jacob Levitan
2021 Symmetry  
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.
doi:10.3390/sym13060957 fatcat:b4pbvlsr55gyhoqxjyuds4o3te