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.
Highlights
The study of higher-derivative gravity theories has attracted critical attention in quantum gravity
For given r+ = 1, 2, 4, three horizontal lines M2c which are ending points split unstable (M2 < M2c) and stable (M2 > M2c) black holes. It indicates that the Gregory-Laflamme instability of small black holes in the α = −3β Einstein–Ricci cubic gravity is due to the massiveness (0 < M2 < M2c) of massive spin-2 mode, but not a feature of higher-order gravity giving a ghost
It is known that the correlated stability conjecture proposed by Gubser-Mitra [28] does not hold for the SAdS black hole found in Einstein gravity, but it holds for the SAdS black hole found in Einstein-Weyl gravity [33]
Summary
The study of higher-derivative gravity theories has attracted critical attention in quantum gravity. One does not worry about the ghost (an unhealthy massive spin-2 field) problem arising from the fourth-order gravity because the linearized Ricci tensor δ Rμν as a healthy massive spin-2 field satisfies a second-order equation [25] Visiting this stability issue again, it has shown that the small black hole in Einstein-Weyl gravity is unstable against s(l = 0)-mode Ricci tensor perturbation, while the large black hole is stable against s-mode perturbation [26]. This was performed by comparing the linearized Ricci tensor equation with the linearized metric equation around the five-dimensional black string where the Gregory-Laflamme instability appeared [27]. The effective cosmological constant is related to the bare cosmological constant as
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
