On equation of geodesic deviation and its solutions

TL;DR

This paper discusses the equations of geodesic deviation in 3D and 4D Riemann spaces, presenting exact solutions derived from recent matrix Schrödinger equation results, including specific solutions for Schwarzschild and Kasner metrics.

Contribution

It introduces new exact solutions to geodesic deviation, Raychaudhuri, and generalized Raychaudhuri equations using recent advances in matrix Schrödinger equations.

Findings

Exact solutions for geodesic deviation in Schwarzschild and Kasner metrics

Demonstration of solution classes for Raychaudhuri equations

Application of matrix Schrödinger equation results to differential geometry

Abstract

Equations of geodesic deviation for the 3-dimensional and 4-dimensional Riemann spaces are discussed. Availability of wide classes of exact solutions of such equations, due to recent results for the matrix Schr\"odinger equation, is demonstrated. Particular classes of exact solutions for the geodesic deviation equation as well as for the Raychaudhuri and generalized Raychaudhuri equation are presented. Solutions of geodesic deviation equation for the Schwarzshild and Kasner metrics are found.