Quasitopological Lifshitz black holes

Abstract

We investigate the effects of including a quasitopological cubic curvature term to the Gauss-Bonnet action to five-dimensional Einstein gravity coupled to a Proca field and search for solutions with asymptotically Lifshitz scaling symmetry. We find that a new set of Lifshitz black hole solutions exist that are analogous to those obtained in third-order Lovelock gravity in higher dimensions. No additional matter fields are required to obtain solutions with asymptotic Lifshitz behavior, though we also investigate solutions with matter. Furthermore, we examine black hole solutions and their thermodynamics in this situation and find that a negative quasitopological term, just like a positive Gauss-Bonnet term, prevents instabilities in what are ordinarily unstable Einsteinian black holes.