Instability of Reissner-Nordstr\"om-AdS black hole under perturbations of a scalar field coupled to Einstein tensor

Understand

We study the instability of a Reissner-Nordstr\"om-AdS (RNAdS) black hole under perturbations of a massive scalar field coupled to Einstein tensor.

• Calculating the potential of the scalar perturbations we find that as the strength of the coupling of the scalar to Einstein tensor is increasing, the potential develops a negative well outside the black hole horizon, indicating an instability of the background RNAdS.
• We then investigate the effect of this coupling on the quasinormal modes.
• We find that there exists a critical value of the coupling which triggers the instability of the RNAdS.