Black Hole Entropy and Viscosity Bound in Horndeski Gravity

Abstract

Horndeski gravities are theories of gravity coupled to a scalar field, in which the action contains an additional non-minimal quadratic coupling of the scalar, through its first derivative, to the Einstein tensor or the analogous higher-derivative tensors coming from the variation of Gauss-Bonnet or Lovelock terms. In this paper we study the thermodynamics of the static black hole solutions in $n$ dimensions, in the simplest case of a Horndeski coupling to the Einstein tensor. We apply the Wald formalism to calculate the entropy of the black holes, and show that there is an additional contribution over and above those that come from the standard Wald entropy formula. The extra contribution can be attributed to unusual features in the behaviour of the scalar field. We also show that a conventional regularisation to calculate the Euclidean action leads to an expression for the entropy that disagrees with the Wald results. This seems likely to be due to ambiguities in the subtraction procedure. We also calculate the viscosity in the dual CFT, and show that the viscosity/entropy ratio can violate the $\eta /S\ge 1/(4\pi )$ bound for appropriate choices of the parameters.

30 pages, no figure, minor revisions

References in corpus (10)

• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• Minkowski-space correlators in AdS/CFT correspondence: recipe and applications
• Effect of curvature squared corrections in AdS on the viscosity of the dual gauge theory
• Non-universal shear viscosity from Einstein gravity
• The shear viscosity of gauge theory plasma with chemical potentials
• The shear viscosity of holographic superfluids
• Thermodynamics of Lifshitz Black Holes
• The shear viscosity of the non-commutative plasma
• SU(2)-Colored (A)dS Black Holes in Conformal Gravity
• A modulated shear to entropy ratio

Cited by in corpus (80)

• Horndeski Gravity as $D\to 4$ Limit of Gauss-Bonnet
• Slowly rotating neutron stars in the nonminimal derivative coupling sector of Horndeski gravity
• Momentum transport in strongly coupled anisotropic plasmas in the presence of strong magnetic fields
• Investigating shadow images and rings of the charged Horndeski black hole illuminated by various thin accretions
• Diffusivities bounds and chaos in holographic Horndeski theories
• Rings and images of Horndeski hairy black hole illuminated by various thin accretions
• Thermodynamics of Charged Black Holes in Einstein-Horndeski-Maxwell Theory
• Static and rotating solutions for Vector-Galileon theories
• Holographic Complexity and Two Identities of Action Growth
• Einstein-Vector Gravity, Emerging Gauge Symmetry and de Sitter Bounce
• Dyonic (A)dS Black Holes in Einstein-Born-Infeld Theory in Diverse Dimensions
• Axionic black branes with conformal coupling
• DC Conductivities with Momentum Dissipation in Horndeski Theories
• Holographic Heat Current as Noether Current
• On the Noether charge and the gravity duals of quantum complexity
• Gravitational lensing by a Horndeski black hole
• Holographic Complexity Growth Rate in Horndeski Theory
• Bounce Universe and Black Holes from Critical Einsteinian Cubic Gravity
• Circular orbits and accretion process in a class of Horndeski/Galileon black holes
• Criticality in Einstein-Gauss-Bonnet Gravity: Gravity without Graviton
• On holographic entanglement entropy of Horndeski black holes
• Topological black hole in the theory with nonminimal derivative coupling with power-law Maxwell field and its thermodynamics
• Quasi-Topological Ricci Polynomial Gravities
• AdS/BCFT correspondence and BTZ black hole thermodynamics within Horndeski gravity
• Thermodynamics of Horndeski black holes with non-minimal derivative coupling
• $D=5$ Rotating Black Holes in Einstein-Gauss-Bonnet Gravity: Mass and Angular Momentum in Extremality
• Hairy Taub-NUT/Bolt-AdS solutions in Horndeski theory
• Notes on thermodynamics of Schwarzschild-like bumblebee black hole
• The effect of scalar hair on the charged black hole with the images from accretions disk
• Quasinormal modes, greybody factors and thermodynamics of four dimensional AdS black holes in Critical Gravity
• An a-theorem for Horndeski Gravity at the Critical Point
• Shear viscosity from black holes in generalized scalar-tensor theories in arbitrary dimensions
• Planar black holes configurations and shear viscosity in arbitrary dimensions with shift and reflection symmetric scalar-tensor theories
• Black branes in asymptotically Lifshitz spacetime and viscosity/entropy ratios in Horndeski gravity
• Spinning black holes for generalized scalar tensor theories in three dimensions
• Black holes in vector-tensor theories and their thermodynamics
• Exact formation of hairy planar black holes
• Horndeski Gravity and the Violation of Reverse Isoperimetric Inequality
• Scalar field perturbation around a rotating hairy black hole: quasinormal modes, quasibound states and superradiant instability
• Rotating black hole with a probe string in Horndeski Gravity
• Higher-Derivative Gravity with Non-minimally Coupled Maxwell Field
• Exploring the black hole spectrum of axionic Horndeski theory
• Superradiant energy extraction from rotating hairy Horndeski black holes
• Braneworlds in Horndeski gravity
• Scale Invariance vs. Conformal Invariance: Holographic Two-Point Functions in Horndeski Gravity
• AdS/BCFT correspondence and Horndeski gravity in the presence of gauge fields: holographic paramagnetism/ferromagnetism phase transition
• Spontaneous Momentum Dissipation and Coexistence of Phases in Holographic Horndeski Theory
• Note on Noether charge and holographic transports
• AC charge transport in holographic Horndeski gravity
• Magnetically-Charged Black Branes and Viscosity/Entropy Ratios
• Holographic renormalization of Horndeski gravity
• Exploring the shear viscosity in four-dimensional planar black holes beyond General Relativity
• Violation of Thermal Conductivity Bound in Horndeski Theory
• Magnetized AdS/BCFT Correspondence in Horndeski Gravity
• Quartic Horndeski, planar black holes, holographic aspects and universal bounds
• Perturbations of massless external fields in Horndeski hairy black hole
• Scalar-tensor black holes in an expanding universe
• Covariant conserved currents for scalar-tensor Horndeski theory
• Nuclear and Quark Matter at High Temperature
• Investigating the Linearized Second Law in Horndeski Gravity
• Einstein-Horndeski gravity and the ultra slowly evaporating black hole
• One-loop corrections to $\eta /s$ in AdS${}_4$/CFT${}_3$
• Action Growth of Dyonic Black Holes and Electromagnetic Duality
• Viscosity bound for anisotropic superfluids with dark matter sector
• To stealth or not to stealth: Thermodynamics of stealth black holes
• Gravitational odd-parity perturbation of a Horndeski hairy black hole: quasinormal mode and parameter constraint
• Dissipative processes at the acoustic horizon
• The effect of three matters on KSS bound
• Black branes in asymptotically Lifshitz spacetimes in $\kappa$-deformed Horndeski gravity
• Holographic Boundary Conformal Field Theory within Horndeski Gravity
• Holographic study of shear viscosity and butterfly velocity for magnetic field-driven quantum criticality
• Static Spherically Symmetric solutions in a subclass of Horndeski theories of gravity
• Static topological black hole with nonminimal derivative coupling and nonlinear electromagnetic field of Born-Infeld type
• Deformations of the AdS-Schwarzschild black brane and the shear viscosity of the quark-gluon plasma
• Non-Abelian Exponential Yang-Mills AdS Black Brane and Transport Coefficients
• Cosmological scalar perturbations in Horndeski-like gravity
• Validity of the Background Subtraction Method for Black Hole Thermodynamics in Matter-Coupled Gravity Theories
• Black Hole Zeroth Law in Horndeski Gravity
• Shear viscoelasticity in anisotropic holographic axion model
• A universal relation among Euclidean integrals for black holes in higher-derivative gravity theories