  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.

General Relativity and Quantum Cosmology;Cosmology and Nongalactic Astrophysics;High Energy Physics - Theory