Dynamical evolution of a scalar field coupling to Einstein's tensor in the Reissner-Nordstr\"{o}m black hole spacetime

Understand

We study the dynamical evolution of a scalar field coupling to Einstein's tensor in the background of Reissner-Nordstr\"{o}m black hole.

• Our results show that the the coupling constant $\eta$ imprints in the wave dynamics of a scalar perturbation.
• In the weak coupling, we find that with the increase of the coupling constant $\eta$ the real parts of the fundamental quasinormal frequencies decrease and the absolute values of imaginary parts increase for fixed charge $q$ and multipole number $l$.
• In the strong coupling, we find that for $l\neq0$ the instability occurs when $\eta$ is larger than a certain threshold value $\eta_c$ which deceases with the multipole number $l$ and charge $q$.