Stability analysis of black holes by the $S$-deformation method for coupled systems

TL;DR

This paper introduces an $S$-deformation method to analyze the linear stability of black holes governed by coupled Schrödinger equations, providing a systematic approach to verify stability through Riccati transformations.

Contribution

The paper develops a new $S$-deformation technique for coupled systems, extending stability analysis methods to more complex black hole perturbations.

Findings

Successfully applied the method to specific black hole models.

Numerical results confirm the stability of studied black hole solutions.

The approach simplifies stability proofs for coupled perturbation systems.

Abstract

We propose a simple method to prove the linear mode stability of a black hole when the perturbed field equations take the form of a system of coupled Schr\"odinger equations. The linear mode stability of the spacetime is guaranteed by the existence of an appropriate $S$-deformation. Such an $S$-deformation is related to the Riccati transformation of a solution to the Schr\"odinger system with zero energy. We apply this formalism to some examples and numerically study their stability.