# On generalized quasi-topological cubic-quartic gravity: thermodynamics and holography

## TL;DR

This paper studies the thermodynamics and phase transitions of black holes in generalized quasi-topological gravity with cubic and quartic curvature terms, revealing new critical behaviors and implications for holography and the viscosity-to-entropy ratio.

## Contribution

It introduces a detailed analysis of black hole thermodynamics in higher curvature gravity, identifying conditions for phase transitions and effects on holographic dual properties.

## Key findings

- Multiple critical points in higher dimensions.
- Van der Waals and reverse Van der Waals phase transitions.
- Violation of the KSS bound in five dimensions.

## Abstract

We investigate the thermodynamic behaviour of asymptotically anti de Sitter black holes in generalized quasi-topological gravity containing terms both cubic and quartic in the curvature. We investigate the general conditions required for physical phase transitions and critical behaviour in any dimension and then consider in detail specific properties in spacetime dimensions 4, 5, and 6. We find for spherical black holes that there are respectively at most two and three physical critical points in five and six dimensions. For hyperbolic black holes we find the occurrence of Van der Waals phase transitions in four dimensions and reverse Van der Waals phase transitions in dimensions greater than 4 if both cubic and quartic curvature terms are present. We also observe the occurrence of phase transitions in for fixed chemical potential. We consider some applications of our work in the dual CFT, investigating how the ratio of viscosity to entropy is modified by inclusion of these higher curvature terms. We conclude that the presence of the quartic curvature term results in a violation of the KSS bound in five dimensions, but not in other dimensions.