Static spherically symmetric solutions to a system of generalized Einstein-Maxwell field equations

Abstract

In this paper I investigate the static, spherically symmetric, pure electric, source-free solutions to the most general second-order vector-tensor theory of gravitation and electromagnetism which is such that its field equations are (i) derivable from a variational principle, (ii) consistent with the notion of conservation of charge, (iii) in agreement with Einstein's equations in the absence of electromagnetic fields, and (iv) compatible with Maxwell's equations in a flat space. These solutions (which are given in series form) bear a strong resemblance to the Reissner-Nordstr\"om solution (of the Einstein-Maxwell field equations) in the asymptotic domain; however, they differ quite radically from the Reissner-Nordstr\"om solution in the vicinity of the source. In addition it appears as though many of these solutions are only compatible with electric monopoles of finite extent.