Gravitational Wave Electrodynamics

We derive Maxwell equations for electric and magnetic fields in curved spacetime from first principles. We show that the latter system enjoys an SO(2) duality symmetry, contrary to the results of previous works. We find that in a detector with static background magnetic or electric field, the weak gravity effects are analogous to the effects from a medium composed of both electrically and magnetically charged particles. We show that generation of electromagnetic radiation by gravitational waves in an external magnetic field is four times more efficient than previously believed. We discuss differences between axion and gravitational wave electrodynamics.Comment: minor corrections, acknowledgments updated; results unchange