2024/09/30 by Madhukrishna Chakraborty, Subenoy Chakraborty, Chakraborty, Madhukrishna +1
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Curvature #Fractional Differential Equations Solutions #Geometry #Mathematical analysis #Mathematics #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2409.19900
openalex publication_date 2024/09/30 · openalex created_date 2024/10/28 · openalex updated_date 2026/07/28
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.