Raychaudhuri equation, geometrical flows and geometrical entropy

Lawrence Paul Horwitz; Vishnu S. Namboothiri; K. Gautham Varma; Asher Yahalom; Yosef Strauss; Jacob Levitan

doi:10.3390/sym13060957

Raychaudhuri equation, geometrical flows and geometrical entropy

Lawrence Paul Horwitz, Vishnu S. Namboothiri, K. Gautham Varma, Asher Yahalom, Yosef Strauss, Jacob Levitan

Department of Physics

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

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 transforma-tions. 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.

Original language	English
Article number	957
Journal	Symmetry
Volume	13
Issue number	6
DOIs	https://doi.org/10.3390/sym13060957
State	Published - Jun 2021

Bibliographical note

Publisher Copyright:
© 2021 by the authors. Licensee MDPI, Basel, Switzerland.

Keywords

Chaos theory
Geometrical entropy
Geometrical flow
Kaluza Klein cosmology
Kaluza Klein theory
Raychaudhuri equation
Riccati equation

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AU - Gautham Varma, K.

AU - Yahalom, Asher

AU - Strauss, Yosef

AU - Levitan, Jacob

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KW - Geometrical entropy

KW - Geometrical flow

KW - Kaluza Klein cosmology

KW - Kaluza Klein theory

KW - Raychaudhuri equation

KW - Riccati equation

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Raychaudhuri equation, geometrical flows and geometrical entropy

Abstract

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Keywords

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