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

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.

Thermodynamics of Dyonic NUT Charged Black Holes with entropy as Noether charge

“…The Noether charge entropy (3.5) depends on the parameters (e, g) and is not positive for all values of the parameters. This phenomenon has been seen before in Taub-NUT AdS spacetimes [6,8] as well as in higher-curvature gravity [46,48,49]. While negative entropy does not make sense from a statistical mechanics viewpoint, the LTN solution does not have any pathologies (beyond, perhaps, what we have noted for the Misner string), and there is no obvious reason that these negative entropy solutions should be rejected outright.…”

(Generalized) quasi-topological gravities at all orders

“…The equations determining such solutions for general D and n are precisely the ones obtained in Section 5 here, so it would be interesting to perform a full study of the thermodynamic properties of the black hole solutions of general D and n GQTG and Quasi-topological gravities, along the lines of the one performed in [10] for the D = 4 case. It would also be interesting to study the holographic dictionary for those classes of theories, along the lines of [15,19,20,41,[64][65][66][67].…”

Extremal rotating black holes in Einsteinian cubic gravity

“…x0g(y) ω(1−y 2 ) , which allows for a more direct comparison between the different curves. We have checked that, when x 0 is small enough, the slowly-rotating expansion (39) gives a very good approximation to the numerical curves. Looking at Fig.…”