On generalized quasi-topological cubic-quartic gravity: thermodynamics and holography
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Springer
Received: March 6, Revised: May 13, Accepted: June 20, Published: July 3,
2019 2019 2019 2019
Mozhgan Mira,b and Robert B. Manna,c a
Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada b Department of Physics, Faculty of Science, Ferdowsi University of Mashhad, P.O. Box 1436, Mashhad, Iran c Perimeter Institute, 31 Caroline Street North, Waterloo, ON, N2L 2Y5, Canada
E-mail: [email protected], [email protected] 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. Keywords: Black Holes, AdS-CFT Correspondence ArXiv ePrint: 1902.10906
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP07(2019)012
JHEP07(2019)012
On generalized quasi-topological cubic-quartic gravity: thermodynamics and holography
Contents 1 Introduction
1 4 4 6 7 10
3 Thermodynamic properties 3.1 First law and Smarr relation 3.2 Physical constraints
12 13 16
4 Thermodynamics in the canonical ensemble 4.1 AdS4 vacua and maximum pressure 4.2 Critical behaviour in four dimensions 4.3 Critical behaviour in five dimensions 4.4 Critical behaviour in six dimensions 4.5 Critical behaviour in more than six dimensions
16 17 19 24 30 36
5 Thermodynamics in grand canonical ensemble 5.1 Four dimensions 5.2 Higher dimensions
38 38 40
6 Holographic hydrodynamics
42
7 Discussion
47
A Explicit form of Lagrangian densities
50
B Pad´ e approximants procedure to construct the shooting parameter
50
1
Introduction
In recent years there has been an increased appreciation of the role that higher-curvature theories of gravity play in our understanding of several areas of physics, including supergravity and string theory, holography, cosmology, and black holes. These studies are motivated both by a desire to understand the ultraviolet behaviour of gravity and by a realization that terms non-linear in the curvature generically appear in perturbative calculations,
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