Numerical-relativity Simulations of the Quasi-Circular Inspiral and Merger of Non-Spinning, Charged Black Holes: Methods and Comparison with Approximate Approaches

We present fully general relativistic simulations of the quasicircular inspiral and merger of charged, nonspinning, binary black holes with charge-to-mass ratio lambda <= 0.3. We discuss the key features that enabled long term and stable evolutions of these binaries. We also present a formalism for computing the angular momentum carried away by electromagnetic waves, and the electromagnetic contribution to black-hole horizon properties. We implement our formalism and present the results for the first time in numerical-relativity simulations. In addition, we compare our full nonlinear solutions with existing approximate models for the inspiral and ringdown phases. We show that Newtonian models based on the quadrupole approximation have errors of 20%-400% in key gauge-invariant quantities. On the other hand, for the systems considered, we find that estimates of the remnant black hole spin based on the motion of test particles in Kerr-Newman spacetimes agree with our nonlinear calculations to within a few percent. Finally, we discuss the prospects for detecting black hole charge by future gravitational-wave detectors using either the inspiral-merger-ringdown signal or the ringdown signal alone.