Superradiant instability of charged massive scalar field in Kerr-Newman-anti-de Sitter black hole

TL;DR

This paper analytically investigates the superradiant instability of a charged massive scalar field around small Kerr-Newman-anti-de Sitter black holes, revealing their instability under certain conditions.

Contribution

It provides an analytical solution for the Klein-Gordon equation in this context, demonstrating the instability of small black holes against scalar perturbations with small charge.

Findings

Positive imaginary parts of quasinormal frequencies indicate instability.

Small Kerr-Newman-AdS black holes are unstable to scalar field perturbations.

Analytical matching technique effectively predicts superradiant instability.

Abstract

We study the superradiance instability of charged massive scalar field in the background of Kerr-Newman-anti-de Sitter black hole. By employing the asymptotic matching technique to solve Klein-Gordon equation analytically, the complex parts of quasinormal frequencies are shown to be positive in the regime of superradiance. Because the calculation is performed in the approximation of small black hole, the result indicates that small Kerr-Newman-anti-de Sitter black hole is unstable against the massive scalar field perturbation with small charge.