Deviation of nonradial geodesics in a static spherically symmetric space-time

TL;DR

This paper extends the understanding of tidal forces to non-radial geodesics in static spherically symmetric spacetimes, providing diagonalization methods and explicit solutions in Schwarzschild geometry.

Contribution

It generalizes tidal force analysis to non-radial geodesics and derives explicit solutions considering angular momentum effects.

Findings

Diagonalization of geodesic deviation equation for non-radial motion

Expressions for tidal forces in spherically symmetric metrics

Solutions showing how angular momentum influences geodesic deviation

Abstract

The article generalizes the description of tidal forces to the case of geodesics with non-zero angular momentum in the metric of static spherically symmetric black holes. We show that the geodesic deviation equation can be diagonalized even with non-radial free motion of a test body in the gravitational field. We present expressions for the spatial components of the tidal force in a spherically symmetric metric. We also solve geodesic deviation equation in the Schwarzschild metric and demonstrate how the presence of angular momentum and its magnitude affect the solution.