We have investigated the wave dynamics of a vector field perturbation coupling to the Einstein tensor in the four-dimensional Reissner-Nordström black hole spacetime. Our results show that besides the dependence on the coupling between the vector field and Einstein tensor, the wave dynamic equation of the vector field perturbation strongly depends on the parity of the perturbation itself, which is quite different from that of the usual vector field perturbation without the coupling in the four-dimensional spacetime. Moreover, we also find that the vector field perturbation with odd parity grows with an exponential rate if the coupling strength is stronger than a certain critical value. However, the vector field perturbation with even parity always decays in the Reissner-Nordström black hole spacetime.

• Received 27 August 2014

DOI:https://doi.org/10.1103/PhysRevD.90.124059