Non-minimal $R^\beta F^2$-Coupled Electromagnetic Fields to Gravity and Static, Spherically Symmetric Solutions

Abstract

We investigate non-minimal $R^\beta F^2$-type couplings of electromagnetic fields to gravity. We derive the field equations by a first order variational principle using the method of Lagrange multipliers. Then we present various static, spherically symmetric solutions describing the exterior fields in the vicinity of electrically charged massive bodies.