Quasi-normal modes, bifurcations and non-uniqueness of charged scalar-tensor black holes

TL;DR

This paper investigates the quasinormal modes of charged scalar-tensor black holes, revealing instabilities, bifurcations, and non-uniqueness of solutions, and discusses implications for black hole classification.

Contribution

It demonstrates the existence of scalar-tensor black holes with primary hair bifurcating from general relativistic solutions and analyzes their stability and non-uniqueness.

Findings

Existence of unstable quasinormal modes in certain parameter ranges.

Scalar-tensor black holes with primary hair bifurcate at critical parameters.

Non-uniqueness of hairy black hole solutions and their stability properties.

Abstract

In the present paper we study the scalar sector of the quasinormal modes of charged general relativistic, static and spherically symmetric black holes coupled to nonlinear electrodynamics and embedded in a class of scalar-tensor theories. We find that for certain domain of the parametric space there exist unstable quasinormal modes. The presence of instabilities implies the existence of scalar-tensor black holes with primary hair that bifurcate from the embedded general relativistic black-hole solutions at critical values of the parameters corresponding to the static zero-modes. We prove that such scalar-tensor black holes really exist by solving the full system of scalar-tensor field equations for the static, spherically symmetric case. The obtained solutions for the hairy black holes are non-unique and they are in one to one correspondence with the bounded states of the potential governing the linear perturbations of the scalar field. The stability of the non-unique hairy black holes is also examined and we find that the solutions for which the scalar field has zeros are unstable against radial perturbations. The paper ends with a discussion on possible formulations of a new classification conjecture.