Raychaudhuri equation, geometrical flows and geometrical entropy

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-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 languageEnglish
Article number957
JournalSymmetry
Volume13
Issue number6
DOIs
StatePublished - Jun 2021

Keywords

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

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