We obtain a large class of AdS spacetimes warped with certain internal spaces in 11-dimensional and type IIA or IIB supergravities. The warp factors depend only on the internal coordinates. These solutions arise as the near-horizon geometries of more general semilocalized multi-intersections of p-branes. We achieve this by noting that any sphere ͑or AdS spacetime͒ of dimension greater than 3 can be viewed as a foliation involving S 3 ͑or AdS 3 ). Then the S 3 ͑or AdS 3 ) can be replaced by a three-dimensional lens space ͑or a BTZ black hole͒, which arises naturally from the introduction of a NUT ͑or a pp wave͒ to the M-branes or the D3-brane. We then obtain multi-intersections by performing a Kaluza-Klein reduction or Hopf T-duality transformation on the fiber coordinate of the lens space ͑or the BTZ black hole͒. These geometries provide further possible examples of the AdS/CFT correspondence and of consistent embeddings of lower-dimensional gauged supergravities in Dϭ11 or Dϭ10.

We study black hole solutions in extended gravities with higher-order curvature terms, including conformal and Einstein-Weyl gravities. In addition to the usual AdS vacuum, the theories admit Lifshitz and Schrödinger vacua. The AdS black hole in conformal gravity contains an additional parameter over and above the mass, which may be interpreted as a massive spin-2 hair. By considering the first law of thermodynamics, we find that it is necessary to introduce an associated additional intensive/extensive pair of thermodynamic quantities. We also obtain new Liftshitz black holes in conformal gravity and study their thermodynamics. We use a numerical approach to demonstrate that AdS black holes beyond the Schwarzschild-AdS solution exist in Einstein-Weyl gravity. We also demonstrate the existence of asymptotically Lifshitz black holes in Einstein-Weyl gravity. The Lifshitz black holes arise at the boundary of the parameter ranges for the AdS black holes. Outside the range, the solutions develop naked singularities. The asymptotically AdS and Lifshitz black holes provide an interesting phase transition, in the corresponding boundary field theory, from a relativistic Lorentzian system to a non-relativistic Lifshitz system.

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We investigate the behavior of stationary string configurations on a fivedimensional AdS black hole background which correspond to quark-antiquark pairs steadily moving in an N = 4 super Yang-Mills thermal bath. There are many branches of solutions, depending on the quark velocity and separation as well as on whether Euclidean or Lorentzian configurations are examined.