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arXiv · 2409.19900

Curvature form of Raychaudhuri equation and its consequences: A geometric approach

Madhukrishna Chakraborty·Subenoy Chakraborty
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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.

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Madhukrishna Chakraborty, Subenoy Chakraborty. 2024-09-30. Curvature form of Raychaudhuri equation and its consequences: A geometric approach. https://arxiv.org/abs/2409.19900

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