Non-minimal $R^\beta F^2$-Coupled Electromagnetic Fields to Gravity and   Static, Spherically Symmetric Solutions
  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. 
Tekin Dereli and \"Ozcan Sert
gr-qc