Linear Stability of Dilatonic Black Holes

TL;DR

This paper demonstrates the linear stability of Dilatonic Black Holes in Einstein-Dilaton-Gauss-Bonnet theory, showing they are stable solutions with non-trivial hair, contrary to classical no-hair theorems.

Contribution

It provides a semi-analytic proof of the linear stability of Dilatonic Black Holes with non-trivial dilaton hair in a generalized gravity theory.

Findings

Dilatonic Black Holes are linearly stable under perturbations.

These black holes possess non-trivial dilaton hair.

They are among the few stable black hole solutions beyond General Relativity.

Abstract

In this talk, we recall the most important features of the Dilatonic Black Holes which arise in the framework of the Einstein-Dilaton-Gauss-Bonnet theory and which are dressed with a classical long range dilaton field in contradiction with the existing "no-hair" theorems of the Theory of General Relativity. We demonstrate linear stability of these black hole solutions under small spacetime-dependent perturbations by making use of a semi-analytic method based on the Fubini-Sturm's theorem. As a result, the Dilatonic Black Holes constitute one of the very few examples of stable black hole solutions with non-trivial "hair" that arise in the framework of a more generalised theory of gravity.