The FGK formalism for black p-branes in d dimensions

We present a generalization to an arbitrary number of spacetime (d) and worldvolume (p+1) dimensions of the formalism proposed by Ferrara, Gibbons and Kallosh to study black holes (p=0) in d=4 dimensions. We include the special cases in which there can be dyonic and self- or anti-self-dual black branes. Most of the results valid for 4-dimensional black holes (relations between temperature, entropy and non-extremality parameter, and between entropy and black-hole potential on the horizon) are straightforwardly generalized. We apply the formalism to the case of black strings in N=2,d=5 supergravity coupled to vector multiplets, in which the black-string potential can be expressed in terms of the dual central charge and work out an explicit example with one vector multiplet, determining supersymmetric and non-supersymmetric attractors and constructing the non-extremal black-string solutions that interpolate between them.