Lovelock black p-branes with fluxes

TL;DR

This paper develops flux compactifications of Lovelock gravity theories over product spaces, enabling the construction of lower-dimensional effective theories and black hole solutions within these frameworks.

Contribution

It introduces a method to achieve flux compactifications of Lovelock gravity using non-minimally coupled p-forms, extending to any Lovelock theory and dimensions.

Findings

Explicit flux compactification formulas for Einstein-Gauss-Bonnet theory.

Construction of black hole solutions in the effective lower-dimensional theory.

Generalization of compactification procedures to all Lovelock theories.

Abstract

In this paper we construct compactifications of generic, higher curvature Lovelock theories of gravity over direct product spaces of the type $\mathcal{M}_D=\mathcal{M}_d \times \mathcal{S}^p $, with $D=d+p$ and $d\ge5$, where $\mathcal{S}^p$ represents an internal, Euclidean manifold of positive constant curvature. We show that this can be accomplished by including suitable non-minimally 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 one and two-form fundamental fields, and provide as well the formulae that allows 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 compactfied manifold, allowing therefore to find, in the Einstein-Gauss-Bonnet case, black holes in the Boulware-Deser family.