Generation of Initial Data for General-Relativistic Simulations of Charged Black Holes

Abstract

Einstein–Maxwell theory is a description of electromagnetism and gravity from first principles that has yielded several interesting results on black holes with electromagnetic fields. However, since astrophysically-relevant black holes are believed to have negligible electric charge, the theory has been mostly confined within the realm of theoretical investigation. In addition to this, this theory has been studied mostly with analytical tools, which is why the vast majority of available results are restricted to spacetimes endowed with some degree of symmetry (e.g., stationarity and axisymmetry). Consequently, dynamical solutions (where no symmetry is assumed), for which the numerical approach is the only feasible one, represent a largely unexplored territory.

In this paper we present our efforts towards dynamical solutions of the coupled Einstein–Maxwell equations. As a first step, we solve numerically the constraint equations to generate valid initial data for dynamical general-relativistic simulations of generic configurations of black holes that possess electric charge, linear and angular momenta. The initial data are constructed with the conformal transverse-traceless approach, and the black holes are described as punctures within a modified Bowen–York framework. The attribution of physical parameters (mass, charge, and momenta) to the holes is performed by adopting the theory of isolated horizons. We implement our new formalism numerically and find it both to be in agreement with previous results and to show good convergence properties.