Gravity and Electromagnetism with $Y(R)F^2$-type Coupling and Magnetic Monopole Solutions

We investigate $Y(R) F^2$-type coupling of electromagnetic fields to gravity. After we derive field equations by a first order variational principle from the Lagrangian formulation of the non-minimally coupled theory, we look for static, spherically symmetric, magnetic monopole solutions. We point out that the solutions can provide possible geometries which may explain the flatness of the observed rotation curves of galaxies.