Particle Dynamics on Test Papapetrou Fields of Vacuum Spacetimes

Abstract

In this paper we examine the dynamics of particles subjected to test Papapetrou fields of vacuum spacetimes. The staring point of our analysis is based on fundamental electrodynamics which emerge from spacetime isometries of a Kerr and Schwarzschild black holes. Taking into account Killing vectors which satisfy Maxwell equations we evaluate the corresponding electric and magnetic fields -- Papapetrou fields -- by fixing proper frames of reference in each spacetime. A timelike observer is considered for the case of a Schwarzschild spacetime while a locally non-rotating (LNR) frame of reference is fixed for a Kerr black hole. In order to probe for the effect of such electromagnetic fields we study the motion of charged test particles in the equatorial plane of both spacetimes. For the case of a Schwarzschild black hole we show that massive/charged test particles may populate the unstable photon sphere for a given domain of the parametric space. Restricting ourselves to orbits with LNR initial conditions for the case of a Kerr black hole we show that there is an explicit deviation between orbits of neutral and charged particles in the case of repulsive configurations. For critical charge-mass ratios $\zeta_*$ test particles can be found in the Kerr retrograde photon sphere thus assigning a physical signature to Papapetrou fields.