Mass-induced instability of SAdS black hole in Einstein-Ricci cubic gravity

TL;DR

This paper investigates the stability of Schwarzschild-AdS black holes in Einstein-Ricci cubic gravity, revealing mass-induced instabilities for small black holes due to Ricci tensor perturbations, and confirms the correlated stability conjecture.

Contribution

It demonstrates the mass-induced instability mechanism for small black holes in Einstein-Ricci cubic gravity and verifies the correlated stability conjecture through entropy calculations.

Findings

Small black holes exhibit Ricci tensor perturbation instabilities.

Massiveness in linearized gravity causes the instability, not ghost states.

The correlated stability conjecture is validated via Wald entropy.

Abstract

We perform the stability analysis of Schwarzschild-AdS (SAdS) black hole in the Einstein-Ricci cubic gravity. It shows that the Ricci tensor perturbations exhibit unstable modes for small black holes. We call this the mass-induced instability of SAdS black hole because the instability of small black holes arises from the massiveness in the linearized Einstein-Ricci cubic gravity, but not a feature of higher-order derivative theory giving ghost states. Also, we point out that the correlated stability conjecture holds for the SAdS black hole by computing the Wald entropy of SAdS black hole in Einstein-Ricci cubic gravity.