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

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