Instability and no-hair paradigm in d-dimensional charged-AdS black holes

TL;DR

This paper investigates whether the no-hair paradigm holds for small charged AdS black holes in higher dimensions with conformally invariant Maxwell fields, finding that scalar hair solutions are not supported in this context.

Contribution

It provides numerical evidence that small charged AdS black holes in higher dimensions do not develop scalar hair under conformally invariant Maxwell perturbations.

Findings

Scalar hairy solutions exist for certain horizon topologies in higher dimensions.

The solutions cannot be considered as scalar hairs on Reissner-Nordstrom backgrounds.

The no-hair paradigm is supported for these black holes in the studied setting.

Abstract

Is it possible the no-hair paradigm is violated when a black hole undergoes an instability? Employing massless charged scalar perturbations, we address this question within the context of conformally invariant Einstein-Maxwell theory for some allowed $d$-dimensional ($d=4n+4$ with conformal parameter $n=0,1,2,...$ ) topological small AdS black-holes. We provide numerical analyses that show the non trivial scalar hairy black hole solutions to include planar and spherical horizon topologies in higher dimensions with an even conformal parameter $n$. It is also shown that the solutions presented here cannot be considered as scalar hairs for a Reissner-Nordstrom background. As a result, for $d$-dimensional small AdS black holes in the presence of a conformally invariant Maxwell source, the no-scalar hair paradigm seems to be supported.