Using the blackfold approach, we study new classes of higher-dimensional rotating black holes with electric charges and string dipoles, in theories of gravity coupled to a 2-form or 3-form field strength and to a dilaton with arbitrary coupling. The method allows to describe not only black holes with large angular momenta, but also other regimes that include charged black holes near extremality with slow rotation. We construct explicit examples of electric rotating black holes of dilatonic and non-dilatonic Einstein-Maxwell theory, with horizons of spherical and non-spherical topology. We also find new families of solutions with string dipoles, including a new class of prolate black rings. Whenever there are exact solutions that we can compare to, their properties in the appropriate regime are reproduced precisely by our solutions. The analysis of blackfolds with string charges requires the formulation of the dynamics of anisotropic fluids with conserved string-number currents, which is new, and is carried out in detail for perfect fluids. Finally, our results indicate new instabilities of near-extremal, slowly rotating charged black holes, and motivate conjectures about topological constraints on dipole hair.

The gamma function Γ(z + 1) = П(z) has been defined in different ways:(1)(Weierstrass)(2)(Kuler)(3)(Gauss)(4)(Euler)(5)(Lerch)

Abstract:We obtain the complete superconformal symmetry transformations on the worldvolume of a D3-brane in an AdS 5 × S 5 background by using a coset superspace approach. We show that in the large R-limit we recover all supersymmetries present on the worldvolume of a D3-brane in a Minkowski background, in particular the Volkov-Akulov supersymmetry. We conclude with a proposal for a scheme to construct higher derivative invariants in D = 4, N = 4 settings.

We consider solutions of massive IIA supergravity corresponding to the half-BPS intersection of D8/D4-branes with fundamental strings. The 1 + 1-dimensional intersection preserves the symmetry D(2, 1; γ; 1) × SO(4). We give a reduction and partial integration of the BPS equations for this symmetry group. We then specialize to the cases of enhanced supersymmetry corresponding to γ = −1/2, −2 or γ = 1. In the first case, we show that the only solution with enhanced symmetry is given by the AdS 6 geometry describing the near horizon geometry of D8/D4-branes in the presence of an O8-plane. In the second case, we identify novel solutions corresponding to fundamental strings ending on D8-branes and a second set of novel solutions corresponding to fundamental strings ending on an O8-plane. In both cases, the fundamental string geometry contains an asymptotically flat region where the string coupling goes to zero. We also show that there are no solutions corresponding to 1+0-dimensional CFTs, which one may have hoped to construct by suspending fundamental strings between D8-branes.