Motion of charged particle in Reissner-Nordstrom spacetime: A Jacobi metric approach

TL;DR

This paper investigates the motion of neutral and charged particles in Reissner-Nordstrom spacetime using the Jacobi metric, highlighting the effects of charge interactions and classifying trajectories via energy-dependent Gaussian curvature.

Contribution

It introduces a Jacobi metric approach to analyze particle trajectories in Reissner-Nordstrom spacetime, especially for particles with charges of same sign as the black hole.

Findings

Derived constant energy paths using variational principles.

Identified the role of Gaussian curvature in trajectory classification.

Analyzed the interplay of gravitational and Coulomb forces for charged particles.

Abstract

The present work discusses motion of neutral and charged particles in Reissner - Nordstrom spacetime. The constant energy paths are derived in a variational principle framework using the Jacobi metric which is parameterized by conserved particle energy. Of particular interest is the case of particle charge and Reissner-Nordstrom black hole charge being of same sign since this leads to a clash of opposing forces - gravitational (attractive) and Coulomb (repulsive). Our paper aims to compliment the recent works of Pugliese, Quevedo and Ruffini [1,2]. The energy dependent Gaussian curvature (induced by Jacobi metric), plays an important role in classifying the trajectories.