Bernstein spectral method for quasinormal modes of a generic black hole spacetime and application to instability of dilaton-de Sitter solution

TL;DR

This paper introduces an improved Bernstein spectral method implemented in Mathematica for calculating quasinormal modes of various black holes, and applies it to analyze the superradiant instability of a charged scalar field in a dilaton-de Sitter black hole background.

Contribution

It develops an efficient computational approach for quasinormal modes applicable to diverse black hole spacetimes and investigates the instability caused by a charged scalar field in a specific black hole model.

Findings

The method effectively detects unstable modes, especially purely imaginary ones.

The instability is confirmed to be superradiant in nature.

The dilaton field significantly affects the instability region.

Abstract

We present the improved Mathematica code which computes quasinormal frequencies with the help of the Bernstein spectral method for a general class of black holes, allowing for asymptotically flat, de Sitter or anti-de Sitter asymptotic. The method is especially efficient when searching for purely imaginary and unstable modes and here it is used for detecting the instability region of a charged scalar field in the background of the charged asymptotically de Sitter dilatonic black hole. We show that the instability has superradiant nature and the dilaton field essentially influences the region of instability.