Time evolutions of scalar field perturbations in $D$-dimensional Reissner-Nordstr\"om Anti-de Sitter black holes

TL;DR

This paper investigates the time evolution and instability of charged scalar fields around higher-dimensional Reissner-Nordström Anti-de Sitter black holes, confirming superradiance as the cause and identifying rapid exponential growth modes.

Contribution

It provides a detailed time domain analysis of superradiant instability in RNAdS black holes across dimensions, linking time profiles with frequency domain results and demonstrating superradiance as the instability's origin.

Findings

Unstable modes are confirmed to be superradiant.

Time profiles match quasinormal mode predictions.

Rapid exponential growth modes are identified.

Abstract

Reissner-Nordstr\"om Anti-de Sitter (RNAdS) black holes are unstable against the charged scalar field perturbations due to the well-known superradiance phenomenon. We present the time domain analysis of charged scalar field perturbations in the RNAdS black hole background in general dimensions. We show that the instabilities of charged scalar field can be explicitly illustrated from the time profiles of evolving scalar field. By using the Prony method to fit the time evolution data, we confirm the mode that dominates the long time behavior of scalar field is in accordance with the quasinormal mode from the frequency domain analysis. The superradiance origin of the instability can also be demonstrated by comparing the real part of the dominant mode with the superradiant condition of charged scalar field. It is shown that all the unstable modes are superradiant, which is consistent with the analytical result in the frequency domain analysis. Furthermore, we also confirm there exists the rapid exponential growing modes in the RNAdS case, which makes the RNAdS black hole a good test ground to investigate the nonlinear evolution of superradiant instability.