Hai-Shan Liu

Critical Points of D-Dimensional Extended Gravities

We study the parameter space of D-dimensional cosmological Einstein gravity together with quadratic curvature terms. In D>4 there are in general two distinct (anti)-de Sitter vacua. We show that, for an appropriate choice of the parameters, there exists a critical point for one of the vacua, with only massless tensor, but neither massive tensor nor scalar, gravitons. At criticality, the linearized excitations have formally vanishing energy (as do black hole solutions). A further restriction of the parameters gives a one-parameter cosmological Einstein plus Weyl^2 model with a unique vacuum, whose Λ is determined.

Thermodynamical metrics and black hole phase transitions

An important phase transition in black hole thermodynamics is associated with the divergence of the specific heat with fixed charge and angular momenta, yet one can demonstrate that neither Ruppeiner’s entropy metric nor Weinhold’s energy metric reveals this phase transition. In this paper, we introduce a new thermodynamical metric based on the Hessian matrix of several free energy. We demonstrate, by studying various charged and rotating black holes, that the divergence of the specific heat corresponds to the curvature singularity of this new metric. We further investigate metrics on all thermodynamical potentials generated by Legendre transformations and study correspondences between curvature singularities and phase transition signals. We show in general that for a system with n-pairs of intensive/extensive variables, all thermodynamical potential metrics can be embedded into a flat (n,n)-dimensional space. We also generalize the Ruppeiner metrics and they are all conformal to the metrics constructed from the relevant thermodynamical potentials.

Black hole entropy and viscosity bound in Horndeski gravity

A bstractHorndeski 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 η/S ≥ 1/(4π) bound for appropriate choices of the parameters.

Generalized Smarr formula and the viscosity bound for Einstein-Maxwell-dilaton black holes

We study the shear viscosity to entropy ratio

Thermodynamics of Lifshitz black holes

\ensuremath{\eta}/S

Scalar Charges in Asymptotic AdS Geometries

in the boundary field theories dual to black-hole backgrounds in theories of gravity coupled to a scalar field, and generalizations including a Maxwell field and nonminimal scalar couplings. Motivated by the observation in simple examples that the saturation of the

Thermodynamics of Einstein-Proca AdS black holes

\ensuremath{\eta}/S\ensuremath{\ge}1/(4\ensuremath{\pi})

DC conductivities from non-relativistic scaling geometries with momentum dissipation

bound is correlated with the existence of a generalized Smarr relation for the planar black-hole solutions, we investigate this in detail for the general black-hole solutions in these theories, focusing especially on the cases where the scalar field plays a nontrivial role and gives rise to an additional parameter in the space of solutions. We find that a generalized Smarr relation holds in all cases, and in fact it can be viewed as the bulk gravity dual of the statement of the saturation of the viscosity to entropy bound. We obtain the generalized Smarr relation, whose existence depends upon a scaling symmetry of the planar black-hole solutions, by two different but related methods, one based on integrating the first law of thermodynamics, and the other based on the construction of a conserved Noether charge.

Thermodynamics of Charged Black Holes in Einstein-Horndeski-Maxwell Theory

A bstractWe specialize the Wald formalism to derive the thermodynamical first law for static black holes with spherical/torus/hyperbolic symmetries in a variety of supergravities or supergravity-inspired theories involving multiple scalars and vectors. We apply the formula to study the first law of a general class of Lifshitz black holes. We analyse the first law of three exact Lifshitz black holes and the results fit the general pattern. In one example, the first law is TdS + ΦdQ = 0 where (Φ, Q) are the electric potential and charge of the Maxwell field. The unusual vanishing of mass in this specific solution demonstrates that super-extremal charged black holes can exist in asymptotic Lifshitz spacetimes.

ON BLACK HOLE STABILITY IN CRITICAL GRAVITIES

Abstract We show that for n-dimensional Einstein gravity coupled to a scalar field with mass-squared m 0 2 = − n ( n − 2 ) / ( 4 l 2 ) , the first law of thermodynamics of (charged) AdS black holes will be modified by the boundary conditions of the scalar field at asymptotic infinity. Such scalars can arise in gauged supergravities in four and six dimensions, but not in five or seven. The result provides a guiding principle for constructing designer black holes and solitons in general dimensions, where the properties of the dual field theories depend on the boundary conditions.