We extend the topological Kerr-Newman-aDS solutions by including NUT charge and find generalizations of the Robinson-Bertotti solution to the negative cosmological constant case with different topologies. We show how all these solutions can be obtained as limits of the general Plebanski-Demianski solution.We study the supersymmetry properties of all these solutions in the context of gauged N = 2, d = 4 supergravity. Generically they preserve at most 1/4 of the total supersymmetry. In the Plebanski-Demianski case, although gauged N = 2, d = 4 supergravity does not have electric-magnetic duality, we find that the family of supersymmetric solutions still enjoys a sort of electric-magnetic duality in which electric and magnetic charges and mass and Taub-NUT charge are rotated simultaneously.

Performing a Scherk-Schwarz dimensional reduction of D = 11 supergravity on a three-dimensional group manifold we construct five D = 8 gauged maximal supergravities whose gauge groups are the three-dimensional (non-)compact subgroups of SL(3, R). These cases include the Salam-Sezgin SO(3) gauged supergravity. We construct the most general half-supersymmetric domain wall solutions to these five gauged supergravities. The generic form is a triple domain wall solution whose truncations lead to double and single domain wall solutions. We find that one of the single domain wall solutions has zero potential but nonzero superpotential.Upon uplifting to 11 dimensions each domain wall becomes a purely gravitational 1/2 BPS solution. The corresponding metric has a 7 + 4 split with a Minkowski 7metric and a 4-metric that corresponds to a gravitational instanton. These instantons generalize the SO(3) metric of Belinsky, Gibbons, Page and Pope (which includes the Eguchi-Hanson metric) to the other Bianchi types of class A.

We show how the Killing spinors of some maximally supersymmetric supergravity solutions whose metrics describe symmetric spacetimes (including AdS, AdS × S and Hpp-waves) can be easily constructed using purely geometrical and group-theoretical methods. The calculation of the supersymmetry algebras is extremely simple in this formalism.

We present warped metrics which solve Einstein equations with arbitrary cosmological constants in both in upper and lower dimensions. When the lower-dimensional metric is the maximally symmetric one compatible with the chosen value of the cosmological constant, the upper-dimensional metric is also the maximally symmetric one and there is maximal unbroken supersymmetry as well.We then introduce brane sources and find solutions with analogous properties, except for supersymmetry, which is generically broken in the orbifolding procedure (one half is preserved in two special cases), and analyze metric perturbations in these backgroundsIn analogy with the D8-brane we propose an effective (d − 2)-brane action which acts as a source for the RS solution. The action consists of a Nambu-Goto piece and a Wess-Zumino term containing a (d − 1)-form field. It has the standard form of the action for a BPS extended object, in correspondence with the supersymmetry preserved by the solution.

The so-called "massive 11-dimensional supergravity" theory gives, for one Killing vector, Romans' massive 10-dimensional supergravity in 10 dimensions, for two Killing vectors an Sl(2, Z) multiplet of massive 9-dimensional supergravity theories that can be obtained by standard generalized dimensional reduction type IIB supergravity and has been shown to contain a gauged supergravity.We consider a straightforward generalization of this theory to three Killing vectors and a 3 × 3 symmetric mass matrix and show that it gives an Sl(3, Z) multiplet of 8-dimensional supergravity theories that contain an SO(3) gauged supergravity which is, in some way, the dual to the one found by Salam and Sezgin by standard generalized dimensional reduction.