Higher-Derivative Gravity with Non-minimally Coupled Maxwell Field

Understand

We construct higher-derivative gravities with a non-minimally coupled Maxwell field.

• The Lagrangian consists of polynomial invariants built from the Riemann tensor and the Maxwell field strength in such a way that the equations of motion are second order for both the metric and the Maxwell potential.
• We also generalize the construction to involve a generic non-minimally coupled $p$-form field strength.
• We then focus on one low-lying example in four dimensions and construct the exact magnetically-charged black holes.