Lovelock black p-branes with fluxes

In this paper, we construct compactifications of generic, higher-curvature Lovelock theories of gravity over direct product spaces of the type M-D = M(d)xS(p), with D = d + p and d > 5, where S-p represents an internal, Euclidean manifold of positive constant curvature. We show that this can be accomplished by including suitable nonminimally coupled p - 1-form fields with a field strength proportional to the volume form of the internal space. We provide explicit details of this constructions for the Einstein-Gauss-Bonnet theory in d + 2 and d + 3 dimensions by using 1- and 2-form fundamental fields and provide as well the formulas that allow one to construct the same family of compactification in any Lovelock theory from dimension d + p to dimension d. These fluxed compactifications lead to an effective Lovelock theory on the compactified manifold, allowing one therefore to fmd, in the Einstein-Gauss-Bonnet case, black holes in the Boulware-Deser family.