Rotating Black Branes wrapped on Einstein Spaces

We present new rotating black brane solutions which solve Einstein's equations with cosmological constant $\Lambda$ in arbitrary dimension $d$. For negative $\Lambda$, the branes naturally appear in AdS supergravity compactifications, and should therefore play some role in the AdS/CFT correspondence. The spacetimes are warped products of a four-dimensional part and an Einstein space of dimension $d-4$, which is not necessarily of constant curvature. As a special subcase, the solutions contain the higher dimensional generalization of the Kerr-AdS metric recently found by Hawking et al.Comment: 11 pages, RevTeX, no figures, thermodynamical discussion and 2 references adde

Nonextremal black holes in gauged supergravity and the real formulation of special geometry

We give a rather general recipe for constructing nonextremal black hole solutions to N=2, D=4 gauged supergravity coupled to abelian vector multiplets. This problem simplifies considerably if one uses the formalism developed in arXiv:1112.2876, based on dimensional reduction and the real formulation of special geometry. We use this to find new nonextremal black holes for several choices of the prepotential, that generalize the BPS solutions found in arXiv:0911.4926. Some physical properties of these black holes are also discussed.Comment: 26 pages, uses JHEP3.cls. v2: Minor corrections, 1 ref. adde

First order flow equations for nonextremal black holes in AdS (super)gravity

We consider electrically charged static nonextremal black holes in $d$-dimensional Einstein-Maxwell-(A)dS gravity, whose horizon is a generic Einstein space in $d-2$ dimensions. It is shown that for this system the Hamilton-Jacobi equation is exactly solvable and admits two branches of solutions. One of them exhibits a non-simply connected domain of integration constants and does not reduce to the well-known solution for the $d=4$ BPS case. The principal functions generate two first order flows that are analytically different, but support the same general solution. One of the two sets of flow equations corresponds to those found by L\"u, Pope and V\'azquez-Poritz in hep-th/0307001 and (for $d=4$ and $\Lambda=0$) by Miller, Schalm and Weinberg in hep-th/0612308. This clarifies also the reason for the very existence of first order equations for nonextremal black holes, namely, they are just the expressions for the conjugate momenta in terms of derivatives of the principal function in a Hamilton-Jacobi formalism. In the last part of our paper we analyze how much of these integrability properties generalizes to matter-coupled $N=2$, $d=4$ gauged supergravity.Comment: 17 pages. v2: Refs. added. v3: Final version to appear in JHE

Black holes in an expanding universe and supersymmetry

This paper analyzes the supersymmetric solutions to five and six-dimensional minimal (un)gauged supergravities for which the bilinear Killing vector constructed from the Killing spinor is null. We focus on the spacetimes which admit an additional ${\rm SO}(1,1)$ boost symmetry. Upon the toroidal dimensional reduction along the Killing vector corresponding to the boost, we show that the solution in the ungauged case describes a charged, nonextremal black hole in a Friedmann-Lema\^itre-Robertson-Walker (FLRW) universe with an expansion driven by a massless scalar field. For the gauged case, the solution corresponds to a charged, nonextremal black hole embedded conformally into a Kantowski-Sachs universe. It turns out that these dimensional reductions break supersymmetry since the bilinear Killing vector and the Killing vector corresponding to the boost fail to commute. This represents a new mechanism of supersymmetry breaking that has not been considered in the literature before.Comment: 9 pages, 1 figure; v2: minor modifications, published version in PL

Fluid dynamics on ultrastatic spacetimes and dual black holes

We show that the classification of shearless and incompressible stationary fluid flows on ultrastatic manifolds is equivalent to classifying the isometries of the spatial sections. For a flow on R x S$^2$ this leaves only one possibility, since on the 2-sphere all Killing fields are conjugate to each other, and it is well-known that the gravity dual of such a (conformal) fluid is the spherical KNAdS$_4$ black hole. On the other hand, in R x H$^2$ the situation is more complicated, since the isometry group of H$^2$ admits elliptic, parabolic and hyperbolic elements. One might thus ask what the gravity duals of the flows corresponding to these three different cases are. Answering this question is one of the scopes of this paper. In particular we identify the black hole dual to a fluid that is purely translating on the hyperbolic plane. Although this lies within the Carter-Plebanski (CP) class, it has never been studied in the literature before, and represents thus in principle a new black hole solution in AdS$_4$. For a rigidly rotating fluid in R x H$^2$ (holographically dual to the hyperbolic KNAdS$_4$ solution), there is a certain radius where the velocity reaches the speed of light, and thus the fluid can cover only the region within this radius. Quite remarkably, it turns out that the boundary of the hyperbolic KNAdS$_4$ black hole is conformal to exactly that part of R x H$^2$ in which the fluid velocity does not exceed the speed of light. We extend these results to establish a precise mapping between possible flows on ultrastatic spacetimes (with constant curvature spatial sections) and the parameter space of the CP solution. Finally, we show that the alternative description of the hyperbolic KNAdS$_4$ black hole in terms of fluid mechanics on R x S$^2$ or on flat space is dynamical and consists of a contracting or expanding vortex.Comment: 43 pages, many figures. v2: Final version to appear in JHE

Nut-charged black holes in matter-coupled N=2, D=4 gauged supergravity

Using the results of arXiv:0804.0009, where all timelike supersymmetric backgrounds of N=2, D=4 matter-coupled supergravity with Fayet-Iliopoulos gauging were classified, we construct genuine nut-charged BPS black holes in AdS_4 with nonconstant moduli. The calculations are exemplified for the SU(1,1)/U(1) model with prepotential F=-iX^0X^1. The resulting supersymmetric black holes have a hyperbolic horizon and carry two electric, two magnetic and one nut charge, which are however not all independent, but are given in terms of three free parameters. We find that turning on a nut charge lifts the flat directions in the effective black hole potential, such that the horizon values of the scalars are completely fixed by the charges. We also oxidize the solutions to eleven dimensions, and find that they generalize the geometry found in hep-th/0105250 corresponding to membranes wrapping holomorphic curves in a Calabi-Yau five-fold. Finally, a class of nut-charged Nernst branes is constructed as well, but these have curvature singularities at the horizon.Comment: 21 pages, no figures, uses JHEP3.cl

Geometry of Killing spinors in neutral signature

We classify the supersymmetric solutions of minimal $N=2$ gauged supergravity in four dimensions with neutral signature. They are distinguished according to the sign of the cosmological constant and whether the vector field constructed as a bilinear of the Killing spinor is null or non-null. In neutral signature the bilinear vector field can be spacelike, which is a new feature not arising in Lorentzian signature. In the $\Lambda<0$ non-null case, the canonical form of the metric is described by a fibration over a three-dimensional base space that has $\text{U}(1)$ holonomy with torsion. We find that a generalized monopole equation determines the twist of the bilinear Killing field, which is reminiscent of an Einstein-Weyl structure. If, moreover, the electromagnetic field strength is self-dual, one gets the Kleinian signature analogue of the Przanowski-Tod class of metrics, namely a pseudo-hermitian spacetime determined by solutions of the continuous Toda equation, conformal to a scalar-flat pseudo-K\"ahler manifold, and admitting in addition a charged conformal Killing spinor. In the $\Lambda<0$ null case, the supersymmetric solutions define an integrable null K\"ahler structure. In the $\Lambda>0$ non-null case, the manifold is a fibration over a Lorentzian Gauduchon-Tod base space. Finally, in the $\Lambda>0$ null class, the metric is contained in the Kundt family, and it turns out that the holonomy is reduced to ${\rm Sim}(1)\times{\rm Sim}(1)$. There appear no self-dual solutions in the null class for either sign of the cosmological constant.Comment: 40 pages, uses JHEP3.cls. v2: Appendix and ref. added. v3: Published versio