Initial data for general relativistic simulations of multiple electrically charged black holes with linear and angular momenta

A general relativistic, stationary, and axisymmetric black hole in a four-dimensional asymptotically flat spacetime is fully determined by its mass, angular momentum, and electric charge. The expectation that astrophysically relevant black holes do not posses charge has resulted in a limited number of investigations of moving and charged black holes in the dynamical, strong-field gravitational (and electromagnetic) regime, in which numerical studies are necessary. Apart from having a theoretical interest, the advent of multimessenger astronomy with gravitational waves offers new ways to think about charged black holes. In this work, we initiate an exploration of charged binary black holes by generating valid initial data for general relativistic simulations of black hole systems that have generic electric charge and linear and angular momenta. We develop our initial data formalism within the framework of the conformal transversetraceless (Bowen-York) technique using the puncture approach and apply the theory of isolated horizons to attribute physical parameters (mass, charge, and angular momentum) to each hole. We implemented our formalism in the case of a binary system by modifying the publicly available TWOPUNCTURES and QUASILOCALMEASURES codes. We demonstrate that our code can recover existing solutions and that it has excellent self-convergence properties for a generic configuration of two black holes.