Raychaudhuri Equation,Geometrical Flows and Geometrical Entropy
Lawrence Paul Horwitz, Vishnu S Namboothiri, Gautham Varma K, Asher, Yahalom, Yossi Strauss, Jacob Levitan
TL;DR
This paper derives a form of the Raychaudhuri equation using geometric flows, linking geometrical entropy to chaos theory, with applications to cosmology and black holes, revealing a novel connection between chaos and general relativity.
Contribution
It introduces a new formulation of the Raychaudhuri equation through geometric flows and establishes a link between geometrical entropy and chaos theory in spacetime.
Findings
Relation between geometrical entropy and mean geodesic deviation
Connection between chaos theory and general relativity
Application to cosmology and black hole physics
Abstract
Raychaudhuri equation is derived by assuming geometric flow in spacetime 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 present a connection between chaos theory and general relativity.
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