Holographic Heat Current as Noether Current

We employ the Noether procedure to derive a general formula for the radially conserved heat current in AdS planar black holes with certain transverse and traceless perturbations, for a general class of gravity theories. For Einstein gravity, the general higher-order Lovelock gravities and also a class of Horndeski gravities, we derive the boundary stress tensor and show that the resulting boundary heat current matches precisely the bulk Noether current.Comment: Latex, 27 pages, typos corrected, comments added, references adde

Thermodynamics of Einstein-Proca AdS Black Holes

We study static spherically-symmetric solutions of the Einstein-Proca equations in the presence of a negative cosmological constant. We show that the theory admits solutions describing both black holes and also solitons in an asymptotically AdS background. Interesting subtleties can arise in the computation of the mass of the solutions and also in the derivation of the first law of thermodynamics. We make use of holographic renormalisation in order to calculate the mass, even in cases where the solutions have a rather slow approach to the asymptotic AdS geometry. By using the procedure developed by Wald, we derive the first law of thermodynamics for the black hole and soliton solutions. This includes a non-trivial contribution associated with the Proca "charge." The solutions cannot be found analytically, and so we make use of numerical integration techniques to demonstrate their existence.Comment: 35 pages, Improved discussion of cases with logarithmic asymptotic fall off

Generalised Smarr Formula and the Viscosity Bound for Einstein-Maxwell-Dilaton Black Holes

We study the shear viscosity to entropy ratio $\eta/S$ in the boundary field theories dual to black hole backgrounds in theories of gravity coupled to a scalar field, and generalisations including a Maxwell field and non-minimal scalar couplings. Motivated by the observation in simple examples that the saturation of the $\eta/S\ge 1/(4\pi)$ bound is correlated with the existence of a generalised 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 non-trivial role and gives rise to an additional parameter in the space of solutions. We find that a generalised 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 generalised 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.Comment: Latex, 36 pages, references added, typos corrected, to appear in PR

Magnetically-Charged Black Branes and Viscosity/Entropy Ratios

We consider asymptotically-AdS $n$-dimensional black brane solutions in a theory of gravity coupled to a set of $N$ $p$-form field strengths, in which the field strengths carry magnetic charges. For appropriately chosen charges, the metrics are isotropic in the $(n-2)$ transverse directions. However, in general the field strength configurations break the full Euclidean symmetry of the $(n-2)$-dimensional transverse space. We then study the linearised equation for transverse traceless metric perturbations in these backgrounds, and by employing the Kubo formula we obtain expressions for $\eta/S$, the ratio of shear viscosity to entropy density. We find that the KSS bound on the ratio $\eta/S$ is generally violated in these solutions. We also extend the discussion by including also a dilatonic scalar field in the theory, leading to solutions that are asymptotically Lifshitz with hyperscaling violation.Comment: References added. 21 page

Supersymmetric Solutions in Four-Dimensional Off-Shell Curvature-Squared Supergravity

Off-shell formulations of supergravities allow one to add closed-form higher-derivative super-invariants that are separately supersymmetric to the usual lower-derivative actions. In this paper we study four-dimensional off-shell N=1 supergravity where additional super-invariants associated with the square of the Weyl tensor and the square of the Ricci scalar are included. We obtain a variety of solutions where the metric describes domain walls, Lifshitz geometries, and also solutions of a kind known as gyratons. We find that in some cases the solutions can be supersymmetric for appropriate choices of the parameters. In some solutions the auxiliary fields may be imaginary. One may reinterpret these as real solutions in an analytically-continued theory. Since the supersymmetry transformation rules now require the gravitino to be complex, the analytically-continued theory has a "fake supersymmetry" rather than a genuine supersymmetry. Nevertheless, the concept of pseudo-supersymmetric solutions is a useful one, since the Killing spinor equations provide first-order equations for the bosonic fields.Comment: 28 page