The initial value problem for electromagnetic source in black-hole space-time

Abstract

There are well-known and well-established methods to solve numerically electromagnetic wave equations in flat space-time in electrical engineering field. We wili apply these well-established methods to solve Einstein-Maxwell equations in general coordinate systems. In this series of works, we want to develop a robust numerical method solving electromagnetic wave propagation in strong gravitational field, that is, in curved space-time. In this paper, we will concentrate how one can generate consitent initial data with specific electromagnetic field around a Schwarzschild black hole. Especially, we will find the initial data for the spherically symmetric configuration. The other more general configurations will be presented elsewhere. Thus, the very simple spherically symmetric configuration, can be possibly applied to dyadosphere model for gamma-ray burst (GRB) internal engine.