Asymptotically AdS-Schwarzschild black hole in Pure-Lovelock theory in 3+1-dimensions

Abstract

Parallel to the new developments in Lovelock gravity, we introduce a general solution to the pure-Lovelock theory in 3+1-dimensional static and spherically symmetric spacetime. The solutions are presented in the presence and absence of a cosmological constant. The solution with a cosmological constant is singular and depending on the values of the free parameters may admit horizons. The solution without a cosmological constant is also singular with a possible cosmological horizon. In the specific third-order pure-Lovelock gravity without a cosmological constant, the solution contains the so-called Rindler acceleration. In the odd p order-pure Lovelock theory with a cosmological constant, there is a class of asymptotically AdS-Schwarzschild black holes. We study the thermal stability of this class of black holes. In comparison with the standard AdS-Schwarzschild black hole (corresponding to the first-order pure Lovelock theory), the higher-order provides a different thermal stability profile which suggests that they are thermally more stable.