Initial data for general-relativistic simulations of generic black hole systems with electric charge, linear and angular momenta

A quantity that has not received much attention in general-relativistic simulations of black holes is the electric charge. As a result, the dynamics of charged black holes in strong-field gravity and electromagnetism remains territory largely unexplored. One approach to tackling this problem is via the $3+1$ formulation of the coupled Einstein-Maxwell equations, where the spacetime and electromagnetic fields are found by evolving forward in time from an initial time slice. In this talk we present our work on generating valid initial data that describe $N$ black holes with electric charge, linear and angular momenta in the $3+1$ decomposition of spacetime. This is achieved by solving the Einstein and Maxwell constraint equations via the conformal transverse-traceless (Bowen-York) technique and treating the physical singularities as punctures. The electromagnetic fields are obtained from a superposition of boosted and rotated Kerr-Newman fields. Once the constraints are solved, we attribute the black hole physical parameters (mass, charge, and momenta) by applying the theory of dynamical horizons. Finally, we present our numerical implementation and results obtained for the case of two black holes.