Quasi-Topological Lifshitz Black Holes

TL;DR

This paper explores how adding a quasi-topological cubic curvature term to five-dimensional Lifshitz gravity yields new black hole solutions, affecting their stability and thermodynamics without needing extra matter fields.

Contribution

It introduces novel Lifshitz black hole solutions with quasi-topological terms, extending previous higher-dimensional theories and analyzing their thermodynamic stability.

Findings

New Lifshitz black hole solutions found with quasi-topological terms.

Negative quasi-topological terms prevent black hole instabilities.

Solutions do not require additional matter fields for asymptotic Lifshitz behavior.

Abstract

We investigate the effects of including a quasi-topological cubic curvature term to the Gauss-Bonnet action to five dimensional Lifshitz gravity. 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 behaviour, though we also investigate solutions with matter. Furthermore, we examine black hole solutions and their thermodynamics in this situation and find that a negative quasi-topological term, just like a positive Gauss-Bonnet term, prevents instabilities in what are ordinarily unstable Einsteinian black holes.