Time domain analysis of superradiant instability for the charged stringy black hole-mirror system

TL;DR

This paper conducts a time domain analysis of superradiant instability in a charged stringy black hole-mirror system, confirming the growth of unstable modes and providing insights into nonlinear development.

Contribution

It introduces a time domain numerical approach to study superradiant instability, complementing previous frequency domain analyses for charged stringy black holes.

Findings

Unstable modes are confirmed via time evolution and Fourier analysis.

Rapid growth modes demonstrate the potential for nonlinear development.

The method validates frequency domain results through time domain simulations.

Abstract

It has been proved that the charged stringy black holes are stable under the perturbations of massive charged scalar fields. However, superradiant instability can be generated by adding the mirror-like boundary condition to the composed system of charged stringy black hole and scalar field. The unstable boxed quasinormal modes have been calculated by using both analytical and numerical method. In this paper, we further provide a time domain analysis by performing a long time evolution of charged scalar field configuration in the background of the charged stringy black hole with the mirror-like boundary condition imposed. We have used the ingoing Eddington-Finkelstein coordinates to derive the evolution equation, and adopted Pseudo-spectral method and the forth-order Runge-Kutta method to evolve the scalar field with the initial Gaussian wave packet. It is shown by our numerical scheme that Fourier transforming the evolution data coincides well with the unstable modes computed from frequency domain analysis. The existence of the rapid growth mode makes the charged stringy black hole a good test ground to study the nonlinear development of superradiant instability.