Gravitational waves on charged black hole backgrounds in modified gravity

The stability of Reissner–Nördstrom black holes with an extremal mass–charge relation was determined by calculating the propagation speed of gravitational waves on this background in an effective field theory (EFT) of gravity. New results for metric components are shown, along with the corresponding new extremal relation, part of which differs by a global factor of 2 from the past published work. This new relation further develops the existing constraints on EFT parameters. The radial propagation speed for gravitational waves in the Regge–Wheeler gauge was calculated linearly for all perturbations, yielding exact luminality for all dimension-4 operators. The dimension-6 radial speed modifications introduce no constraints on the sign of the modified theory parameters from causality arguments, while the deviation from classical theories vanishes at both horizons. The angular speed was found to be altered for the dimension-4 operators, with possible new constraints on the modified theory being suggested from causality arguments. Results are consistent with existing literature on Schwarzschild black hole backgrounds, with some EFT terms becoming active only in non-vacuum spacetimes such as Reissner–Nördstrom black holes.