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

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 complement the recent work of Pugliese et al. (Eur Phys JC77:206. arXiv:1304.2940, 2017; PhysRevD 88:024042. arXiv:1303.6250, 2013). The energy dependent Gaussian curvature (induced by the Jacobi metric) plays an important role in classifying the trajectories.