The motion of a charged black hole in an electromagnetic field

Abstract
The motion of a charged black hole in a weak, asymptotically uniform electric field is analysed by using the Hamiltonian formalism for coupled electromagnetic and gravitational perturbations of the Reissner-Nordstrom space-time. The hole is shown to accelerate with respect to a distant inertial observer according to Newton’s law. The relation of the approximate solution obtained to the exact solution of Ernst, representing the charged C-metric without nodal singularity, is then clarified.