Curvature form of Raychaudhuri equation and its consequences: A geometric approach
General Relativity and Quantum Cosmology
2024-10-01 v1
Abstract
The paper aims at deriving a curvature form of the famous Raychaudhuri equation (RE) and the associated criteria for focusing of a hyper-surface orthogonal congruence of time-like geodesic. Moreover, the paper identifies a transformation of variable related to the metric scalar of the hyper-surface which converts the first order RE into a second order differential equation that resembles an equation of a Harmonic oscillator and also gives a first integral that yields the analytic solution of the RE and Lagrangian of the dynamical system representing the congruence.
Keywords
Cite
@article{arxiv.2409.19900,
title = {Curvature form of Raychaudhuri equation and its consequences: A geometric approach},
author = {Madhukrishna Chakraborty and Subenoy Chakraborty},
journal= {arXiv preprint arXiv:2409.19900},
year = {2024}
}