Correlated stability conjecture for AdS black holes in higher dimensional Ricci cubic gravity

TL;DR

This paper examines the stability of AdS black holes in higher-dimensional Ricci cubic gravity, confirming the correlated stability conjecture by linking thermodynamic and dynamical instabilities, and discovering a new non-AdS black hole solution.

Contribution

It demonstrates the validity of the correlated stability conjecture for these black holes and introduces a novel non-AdS black hole solution.

Findings

Small AdS black holes exhibit Gregory-Laflamme instability.

Thermodynamic instability correlates with dynamical instability.

A new non-AdS black hole solution is found.

Abstract

We investigate the correlated stability conjecture for AdS black holes obtained from the higher dimensional Ricci cubic gravity. It shows that the Ricci tensor perturbations exhibit unstable modes for small AdS black holes when solving Lichnerowicz equation, leading to Gregory-Laflamme instability. On the other hand, we find that a small black hole is thermodynamically unstable by showing the negative heat capacity. This suggests that the correlated stability conjecture holds for AdS black holes in Ricci cubic gravity. Furthermore, we find a newly non-AdS black hole by solving static Lichnerowicz equations, confirming the threshold mass for Gregory-Laflamme instability.