The FGK formalism for black p-branes in d dimensions

TL;DR

This paper generalizes the FGK formalism for analyzing black p-branes across various dimensions, extending previous 4D results to higher dimensions and applying it to black strings in supergravity.

Contribution

It extends the FGK formalism to arbitrary spacetime and worldvolume dimensions, including dyonic and self-dual black branes, and applies it to black strings in five-dimensional supergravity.

Findings

Generalized relations between temperature, entropy, and potentials for black branes.

Explicit solutions for supersymmetric and non-supersymmetric attractors.

Constructed non-extremal black-string solutions interpolating between attractors.

Abstract

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.