Higher Derivative Corrections to R-charged Black Holes: Boundary Counterterms and the Mass-Charge Relation

We carry out the holographic renormalization of Einstein-Maxwell theory with curvature-squared corrections. In particular, we demonstrate how to construct the generalized Gibbons-Hawking surface term needed to ensure a perturbatively well-defined variational principle. This treatment ensures the absence of ghost degrees of freedom at the linearized perturbative order in the higher-derivative corrections. We use the holographically renormalized action to study the thermodynamics of R-charged black holes with higher derivatives and to investigate their mass to charge ratio in the extremal limit. In five dimensions, there seems to be a connection between the sign of the higher derivative couplings required to satisfy the weak gravity conjecture and that violating the shear viscosity to entropy bound. This is in turn related to possible constraints on the central charges of the dual CFT, in particular to the sign of c-a.Comment: 30 pages. v2: references added, some equations simplifie

Black Holes in Quasi-topological Gravity

We construct a new gravitational action which includes cubic curvature interactions and which provides a useful toy model for the holographic study of a three parameter family of four- and higher-dimensional CFT's. We also investigate the black hole solutions of this new gravity theory. Further we examine the equations of motion of quasi-topological gravity. While the full equations in a general background are fourth-order in derivatives, we show that the linearized equations describing gravitons propagating in the AdS vacua match precisely the second-order equations of Einstein gravity.Comment: 33 pages, 4 figures; two references adde

The entropy of black holes: a primer

After recalling the definition of black holes, and reviewing their energetics and their classical thermodynamics, one expounds the conjecture of Bekenstein, attributing an entropy to black holes, and the calculation by Hawking of the semi-classical radiation spectrum of a black hole, involving a thermal (Planckian) factor. One then discusses the attempts to interpret the black-hole entropy as the logarithm of the number of quantum micro-states of a macroscopic black hole, with particular emphasis on results obtained within string theory. After mentioning the (technically cleaner, but conceptually more intricate) case of supersymmetric (BPS) black holes and the corresponding counting of the degeneracy of Dirichlet-brane systems, one discusses in some detail the ``correspondence'' between massive string states and non-supersymmetric Schwarzschild black holes.Comment: 51 pages, 4 figures, talk given at the "Poincare seminar" (Paris, 6 December 2003), to appear in Poincare Seminar 2003 (Birkhauser

Generalized Weyl solutions in d=5 Einstein-Gauss-Bonnet theory: the static black ring

We argue that the Weyl coordinates and the rod-structure employed to construct static axisymmetric solutions in higher dimensional Einstein gravity can be generalized to the Einstein-Gauss-Bonnet theory. As a concrete application of the general formalism, we present numerical evidence for the existence of static black ring solutions in Einstein-Gauss-Bonnet theory in five spacetime dimensions. They approach asymptotically the Minkowski background and are supported against collapse by a conical singularity in the form of a disk. An interesting feature of these solutions is that the Gauss-Bonnet term reduces the conical excess of the static black rings. Analogous to the Einstein-Gauss-Bonnet black strings, for a given mass the static black rings exist up to a maximal value of the Gauss-Bonnet coupling constant $\alpha'$. Moreover, in the limit of large ring radius, the suitably rescaled black ring maximal value of $\alpha'$ and the black string maximal value of $\alpha'$ agree.Comment: 43 pages, 14 figure

Wilsonian Approach to Fluid/Gravity Duality

The problem of gravitational fluctuations confined inside a finite cutoff at radius $r=r_c$ outside the horizon in a general class of black hole geometries is considered. Consistent boundary conditions at both the cutoff surface and the horizon are found and the resulting modes analyzed. For general cutoff $r_c$ the dispersion relation is shown at long wavelengths to be that of a linearized Navier-Stokes fluid living on the cutoff surface. A cutoff-dependent line-integral formula for the diffusion constant $D(r_c)$ is derived. The dependence on $r_c$ is interpreted as renormalization group (RG) flow in the fluid. Taking the cutoff to infinity in an asymptotically AdS context, the formula for $D(\infty)$ reproduces as a special case well-known results derived using AdS/CFT. Taking the cutoff to the horizon, the effective speed of sound goes to infinity, the fluid becomes incompressible and the Navier-Stokes dispersion relation becomes exact. The resulting universal formula for the diffusion constant $D(horizon)$ reproduces old results from the membrane paradigm. Hence the old membrane paradigm results and new AdS/CFT results are related by RG flow. RG flow-invariance of the viscosity to entropy ratio $\eta /s$ is shown to follow from the first law of thermodynamics together with isentropy of radial evolution in classical gravity. The ratio is expected to run when quantum gravitational corrections are included.Comment: 34 pages, harvmac, clarified boundary conditio

Lovelock gravity from entropic force

In this paper, we first generalize the formulation of entropic gravity to (n+1)-dimensional spacetime. Then, we propose an entropic origin for Gauss-Bonnet gravity and more general Lovelock gravity in arbitrary dimensions. As a result, we are able to derive Newton's law of gravitation as well as the corresponding Friedmann equations in these gravity theories. This procedure naturally leads to a derivation of the higher dimensional gravitational coupling constant of Friedmann/Einstein equation which is in complete agreement with the results obtained by comparing the weak field limit of Einstein equation with Poisson equation in higher dimensions. Our study shows that the approach presented here is powerful enough to derive the gravitational field equations in any gravity theory. PACS: 04.20.Cv, 04.50.-h, 04.70.Dy.Comment: 10 pages, new versio

Comments on Holographic Entanglement Entropy and RG Flows

Using holographic entanglement entropy for strip geometry, we construct a candidate for a c-function in arbitrary dimensions. For holographic theories dual to Einstein gravity, this c-function is shown to decrease monotonically along RG flows. A sufficient condition required for this monotonic flow is that the stress tensor of the matter fields driving the holographic RG flow must satisfy the null energy condition over the holographic surface used to calculate the entanglement entropy. In the case where the bulk theory is described by Gauss-Bonnet gravity, the latter condition alone is not sufficient to establish the monotonic flow of the c-function. We also observe that for certain holographic RG flows, the entanglement entropy undergoes a 'phase transition' as the size of the system grows and as a result, evolution of the c-function may exhibit a discontinuous drop.Comment: References adde

Ultraspinning instability of anti-de Sitter black holes

Myers-Perry black holes with a single spin in d>5 have been shown to be unstable if rotating sufficiently rapidly. We extend the numerical analysis which allowed for that result to the asymptotically AdS case. We determine numerically the stationary perturbations that mark the onset of the instabilities for the modes that preserve the rotational symmetries of the background. The parameter space of solutions is thoroughly analysed, and the onset of the instabilities is obtained as a function of the cosmological constant. Each of these perturbations has been conjectured to represent a bifurcation point to a new phase of stationary AdS black holes, and this is consistent with our results.Comment: 22 pages, 7 figures. v2: Reference added. Matches published versio