The final fate of instability of Reissner-Nordstr\"om-anti-de Sitter black holes by charged complex scalar fields

Understand

We investigate instability of 4-dimensional Reissner-Nordstr\"om-anti-de Sitter (RN-AdS$_4$) black holes with various topologies by charged scalar field perturbations.

• We numerically find that the RN-AdS$_4$ black holes become unstable against the linear perturbations below a critical temperature.
• It is analytically shown that charge extraction from the black holes occurs during the unstable evolution.
• To explore the end state of the instability, we perturbatively construct static black hole solutions with the scalar hair near the critical temperature.