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

We investigate non-minimal $R^βF^2$-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.

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