Collisions of charged black holes

We perform fully non-linear numerical simulations of charged-black-hole collisions, described by the Einstein-Maxwell equations, and contrast the results against analytic expectations. We focus on head-on collisions of non-spinning black holes, starting from rest and with the same charge to mass ratio, Q/M. The addition of charge to black holes introduces a new interesting channel of radiation and dynamics, most of which seem to be captured by Newtonian dynamics and flat-space intuition. The waveforms can be qualitatively described in terms of three stages; (i) an infall phase prior to the formation of a common apparent horizon; (ii) a nonlinear merger phase which corresponds to a peak in gravitational and electromagnetic energy; (iii) the ringdown marked by an oscillatory pattern with exponentially decaying amplitude and characteristic frequencies that are in good agreement with perturbative predictions. We observe that the amount of gravitational-wave energy generated throughout the collision decreases by about three orders of magnitude as the charge-to-mass ratio Q/M is increased from 0 to 0.98. We interpret this decrease as a consequence of the smaller accelerations present for larger values of the charge. In contrast, the ratio of energy carried by electromagnetic to gravitational radiation increases, reaching about 22% for the maximum Q/M ratio explored, which is in good agreement with analytic predictions.