Raychaudhuri equation, geometrical flows and geometrical entropy

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

Tel Aviv University, Bar-Ilan University, Ariel University, Ben-Gurion University of the Negev

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

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 - 1 Jun 2021

Keywords

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

All Science Journal Classification (ASJC) codes

Computer Science (miscellaneous)
Chemistry (miscellaneous)
General Mathematics
Physics and Astronomy (miscellaneous)

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10.3390/sym13060957

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title = "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 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.",

keywords = "Chaos theory, Geometrical entropy, Geometrical flow, Kaluza Klein cosmology, Kaluza Klein theory, Raychaudhuri equation, Riccati equation",

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AU - Horwitz, Lawrence

AU - Namboothiri, Vishnu S.

AU - Gautham Varma, K.

AU - Yahalom, Asher

AU - Strauss, Yosef

AU - Levitan, Jacob

PY - 2021/6/1

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N2 - 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.

AB - 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.

KW - Chaos theory

KW - Geometrical entropy

KW - Geometrical flow

KW - Kaluza Klein cosmology

KW - Kaluza Klein theory

KW - Raychaudhuri equation

KW - Riccati equation

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JO - Symmetry

JF - Symmetry

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M1 - 957

ER -

Raychaudhuri equation, geometrical flows and geometrical entropy

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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