Motion of an electrically or magnetically charged body with possibly strong internal gravity through external electromagnetic and gravitational fields

Abstract

This calculation uses matched asymptotic expansions to show, directly from the Einstein-Maxwell equations, that a small charged body with possibly strong internal gravity moves through an electrovac region of a curved, and not necessarily asymptotically flat, external spacetime approximately according to the Lorentz force law. The dimensionless parameter $\ensuremath{\epsilon}\ensuremath{\equiv}\frac{m}{L}$ (where $m$ is the body's mass and $L$ is a curvature reference length of the external field) is assumed small, and it is found that $O(L)$ deviations from the Lorentz force law vanish over times of $O(L)$; deviations of $O(L)$ would be expected to arise only over times of $O(\frac{L}{\ensuremath{\epsilon}})$ or longer. This calculation differs from previous work in that the body may have strong internal gravity (e.g., a charged black hole), its moments are unrestricted, and the external gravitational field need not be asymptotically flat.