We present two new classes of dyonic anti-de Sitter black hole solutions of 4-dimensional maximal N = 8, SO(8) gauged supergravity. They are: (1) static black holes of N = 2, U(1) 4 gauged supergravity with 4 electric and 4 magnetic charges, with spherical, planar or hyperbolic horizons; and (2) rotating black holes of N = 2, U(1) 2 gauged supergravity with 2 electric and 2 magnetic charges. We study their thermodynamics, and point out that the formulation of a consistent thermodynamics for dyonic anti-de Sitter black holes is dependent on the existence of boundary conditions for the gauge fields. We identify several distinct classes of boundary conditions for gauge fields in U (1) 4 supergravity. We study a general family of metrics containing the rotating solutions, and find Killing-Yano tensors with torsion in two conformal frames, which underlie separability.

We study exact solutions of three-dimensional gravity with a cosmological constant and a gravitational Chern-Simons term: the theory known as topologically massive gravity.After reviewing the algebraic classification, we show that if a solution has curvature of algebraic type D, then it is biaxially squashed AdS 3 . Applying the classification, we provide a comprehensive review of the literature, showing that most known solutions are locally equivalent to biaxially squashed AdS 3 or to AdS pp-waves.

We extend the investigation of the recently proposed Kerr/CFT correspondence to large classes of rotating black hole solutions in gauged and ungauged supergravities. The correspondence, proposed originally for four-dimensional Kerr black holes, asserts that the quantum states in the near-horizon region of an extremal rotating black hole are holographically dual to a two-dimensional chiral theory whose Virasoro algebra arises as an asymptotic symmetry of the near-horizon geometry. In fact, in dimension D there are [(D − 1)/2] commuting Virasoro algebras. We consider a general canonical class of near-horizon geometries in arbitrary dimension D, and show that in any such metric the [(D − 1)/2] central charges each imply, via the Cardy formula, a microscopic entropy that agrees with the Bekenstein-Hawking entropy of the associated extremal black hole. In the remainder of the paper we show for most of the known rotating black hole solutions of gauged supergravity, and for the ungauged supergravity solutions with four charges in D = 4 and three charges in D = 5, that their extremal near-horizon geometries indeed lie within the canonical form. This establishes that, in all these examples, the microscopic entropies of the dual CFTs agree with the Bekenstein-Hawking entropies of the extremal rotating black holes.