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

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.