Nonlinear Electrodynamics in General Relativity

General relativistic field equations are derived from a gauge-invariant electromagnetic Lagrangian, which does not involve derivatives of the field, nor any charge density, but otherwise is completely arbitrary. These equations are explicitly solved in the static spherically symmetric case, and it is shown that there are solutions which are everywhere regular and behave, at large distances, like the gravitational and electromagnetic fields of a point charge. Some wave-like solutions are also derived.