Motion of charged particle in Reissner–Nordström spacetime: a Jacobi-metric approach

Abstract

Abstract The present work discusses motion of neutral and charged particles in Reissner–Nordström 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–Nordström 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 complement the recent work of Pugliese et al. (Eur Phys J C 77:206. arXiv:1304.2940 , 2017; Phys Rev D 88:024042. arXiv:1303.6250 , 2013). The energy dependent Gaussian curvature (induced by the Jacobi metric) plays an important role in classifying the trajectories.