Charged Rotating Black Holes in Four-Dimensional Gauged and Ungauged Supergravities

We study four-dimensional non-extremal charged rotating black holes in ungauged and gauged supergravity. In the ungauged case, we obtain rotating black holes with four independent charges, as solutions of N=2 supergravity coupled to three abelian vector multiplets. This is done by reducing the theory along the time direction to three dimensions, where it has an O(4,4) global symmetry. Applied to the reduction of the uncharged Kerr metric, O(1,1)^4\subset O(4,4) transformations generate new solutions that correspond, after lifting back to four dimensions, to the introduction of four independent electromagnetic charges. In the case where these charges are set pairwise equal, we then generalise the four-dimensional rotating black holes to solutions of gauged N=4 supergravity, with mass, angular momentum and two independent electromagnetic charges. The dilaton and axion fields are non-constant. We also find generalisations of the gauged and ungauged solutions to include the NUT parameter, and for the ungauged solutions, the acceleration parameter too. The solutions in gauged supergravity provide new gravitational backgrounds for a further study of the AdS_4/CFT_3 correspondence at non-zero temperature.Comment: Latex, 30 page

Ghost-Free de Sitter Supergravities as Consistent Reductions of String and M-theory

We study properties of supergravity theories with non-compact gaugings, and their higher-dimensional interpretations via consistent reductions on the inhomogeneous non-compact hyperboloidal spaces {\cal H}^{p,q}. The gauged supergravities are free of ghosts, despite the non-compactness of the gauge groups. We give a general discussion of the existence of stationary points in the scalar potentials of such supergravities. These are of interest since they can be associated with de Sitter vacuum configurations. We give explicit results for consistent reductions on {\cal H}^{p,q} in various examples, derived from analytic continuation of previously-known consistent sphere reductions. In addition we also consider black hole and cosmological solutions, for specific examples of non-compact gaugings in D=4,5,7.Comment: Latex, 35 page

Non-Extremal Rotating Black Holes in Five-Dimensional Gauged Supergravity

Supersymmetric black holes in five-dimensional gauged supergravity must necessarily be rotating, and so in order to study the passage to black holes away from supersymmetry, it is of great interest to obtain non-extremal black holes that again have non-zero rotation. In this paper we find a simple framework for describing non-extremal rotating black holes in five-dimensional gauged supergravities. Using this framework, we are able to construct a new solution, describing the general single-charge solution of N=2 gauged supergravity, with arbitrary values for the two rotation parameters. Previously-obtained solutions with two or three equal charges also assume a much simpler form in the new framework, as also does the general solution with three unequal charges in ungauged N=2 supergravity. We discuss the thermodynamics and BPS limit of the new single-charge solutions, and we discuss the separability of the Hamilton-Jacobi and Klein-Gordan equations in these backgrounds.Comment: Latex, 12 pages. Mis-statement about separability of Hamilton-Jacobi and Klein-Gordon equations correcte

Consistent Sphere Reductions and Universality of the Coulomb Branch in the Domain-Wall/QFT Correspondence

We prove that any D-dimensional theory comprising gravity, an antisymmetric n-index field strength and a dilaton can be consistently reduced on S^n in a truncation in which just $n$ scalar fields and the metric are retained in (D-n)-dimensions, provided only that the strength of the couping of the dilaton to the field strength is appropriately chosen. A consistent reduction can then be performed for n\le 5; with D being arbitrary when n\le 3, whilst D\le 11 for n=4 and D\le 10 for n=5. (Or, by Hodge dualisation, $n$ can be replaced by (D-n) in these conditions.) We obtain the lower dimensional scalar potentials and construct associated domain wall solutions. We use the consistent reduction Ansatz to lift domain-wall solutions in the (D-n)-dimensional theory back to D dimensions, where we show that they become certain continuous distributions of (D-n-2)-branes. We also examine the spectrum for a minimally-coupled scalar field in the domain-wall background, showing that it has a universal structure characterised completely by the dimension n of the compactifying sphere.Comment: latex file, 21 pages, 1 figure, minor typo correction

Non-extremal Charged Rotating Black Holes in Seven-Dimensional Gauged Supergravity

We obtain the solution for non-extremal charged rotating black holes in seven-dimensional gauged supergravity, in the case where the three rotation parameters are set equal. There are two independent charges, corresponding to gauge fields in the U(1)xU(1) abelian subgroup of the SO(5) gauge group. A new feature in these solutions, not seen previously in lower-dimensional examples, is that the first-order "odd-dimensional self-duality" equation for the 4-form field strength plays a non-trivial role. We also study the BPS limit of our solutions where the black holes become supersymmetric. Our results are of significance for the AdS_7/CFT_6 correspondence in M-theory.Comment: Latex, 12 pages, typos corrected and a reference adde

Conformal Symmetry of a Black Hole as a Scaling Limit: A Black Hole in an Asymptotically Conical Box

We show that the previously obtained subtracted geometry of four-dimensional asymptotically flat multi-charged rotating black holes, whose massless wave equation exhibit $SL(2,\R) \times SL(2,\R) \times SO(3)$ symmetry may be obtained by a suitable scaling limit of certain asymptotically flat multi-charged rotating black holes, which is reminiscent of near-extreme black holes in the dilute gas approximation. The co-homogeneity-two geometry is supported by a dilation field and two (electric) gauge-field strengths. We also point out that these subtracted geometries can be obtained as a particular Harrison transformation of the original black holes. Furthermore the subtracted metrics are asymptotically conical (AC), like global monopoles, thus describing "a black hole in an AC box". Finally we account for the the emergence of the $SL(2,\R) \times SL(2,\R) \times SO(3)$ symmetry as a consequence of the subtracted metrics being Kaluza-Klein type quotients of $AdS_3\times 4 S^3$. We demonstrate that similar properties hold for five-dimensional black holes.Comment: Sections 3 and 4 significantly augmente

Supersymmetric M3-branes and G_2 Manifolds

We obtain a generalisation of the original complete Ricci-flat metric of G_2 holonomy on R^4\times S^3 to a family with a non-trivial parameter \lambda. For generic \lambda the solution is singular, but it is regular when \lambda={-1,0,+1}. The case \lambda=0 corresponds to the original G_2 metric, and \lambda ={-1,1} are related to this by an S_3 automorphism of the SU(2)^3 isometry group that acts on the S^3\times S^3 principal orbits. We then construct explicit supersymmetric M3-brane solutions in D=11 supergravity, where the transverse space is a deformation of this class of G_2 metrics. These are solutions of a system of first-order differential equations coming from a superpotential. We also find M3-branes in the deformed backgrounds of new G_2-holonomy metrics that include one found by A. Brandhuber, J. Gomis, S. Gubser and S. Gukov, and show that they also are supersymmetric.Comment: Latex, 29 pages. This corrects a previous version in which it was claimed that the M3-brane solutions were pseudo-supersymmetric rather than supersymmetri

Massless 3-brane in M-theory

We construct supersymmetric M3-brane solutions in D=11 supergravity. They can be viewed as deformations of backgrounds taking the form of a direct product of four-dimensional Minkowski spacetime and a non-compact Ricci-flat manifold of G_2 holonomy. Although the 4-form field strength is turned on it carries no charge, and the 3-branes are correspondingly massless. We also obtain 3-branes of a different type, arising as M5-branes wrapped over S^2.Comment: This corrects a previous version in which it was mistakenly claimed that the M3-brane solutions are pseudo-supersymmetric rather than supersymmetri

General Metrics of G_2 Holonomy and Contraction Limits

We obtain first-order equations for G_2 holonomy of a wide class of metrics with S^3\times S^3 principal orbits and SU(2)\times SU(2) isometry, using a method recently introduced by Hitchin. The new construction extends previous results, and encompasses all previously-obtained first-order systems for such metrics. We also study various group contractions of the principal orbits, focusing on cases where one of the S^3 factors is subjected to an Abelian, Heisenberg or Euclidean-group contraction. In the Abelian contraction, we recover some recently-constructed G_2 metrics with S^3\times T^3 principal orbits. We obtain explicit solutions of these contracted equations in cases where there is an additional U(1) isometry. We also demonstrate that the only solutions of the full system with S^3\times T^3 principal orbits that are complete and non-singular are either flat R^4 times T^3, or else the direct product of Eguchi-Hanson and T^3, which is asymptotic to R^4/Z_2\times T^3. These examples are in accord with a general discussion of isometric fibrations by tori which, as we show, in general split off as direct products. We also give some (incomplete) examples of fibrations of G_2 manifolds by associative 3-tori with either T^4 or K3 as base.Comment: Latex, 27 page

Consistent SO(6) Reduction Of Type IIB Supergravity on S^5

Type IIB supergravity can be consistently truncated to the metric and the self-dual 5-form. We obtain the complete non-linear Kaluza-Klein S^5 reduction Ansatz for this theory, giving rise to gravity coupled to the fifteen Yang-Mills gauge fields of SO(6) and the twenty scalars of the coset SL(6,R)/SO(6). This provides a consistent embedding of this subsector of N=8, D=5 gauged supergravity in type IIB in D=10. We demonstrate that the self-duality of the 5-form plays a crucial role in the consistency of the reduction. We also discuss certain necessary conditions for a theory of gravity and an antisymmetric tensor in an arbitrary dimension D to admit a consistent sphere reduction, keeping all the massless fields. We find that it is only possible for D=11, with a 4-form field, and D=10, with a 5-form. Furthermore, in D=11 the full bosonic structure of eleven-dimensional supergravity is required, while in D=10 the 5-form must be self-dual. It is remarkable that just from the consistency requirement alone one would discover D=11 and type IIB supergravities, and that D=11 is an upper bound on the dimension.Comment: Latex, 14 pages, typos corrected and comments adde