Quasitopological electromagnetism: Reissner-Nordström black strings in Einstein and Lovelock gravities

Abstract

In this work, we provide consistent compactifications of Einstein-Maxwell and Einstein-Maxwell-Lovelock theories on direct product spacetimes of the form ${\mathcal{M}}_D={\mathcal{M}}_d\times {\mathcal{K}}^p$, where ${\mathcal{K}}^p$ is a Euclidean internal manifold of constant curvature. For these compactifications to take place, it is required the distribution of a precise flux of $p$-forms over the internal manifold. The dynamic of the $p$-forms are demanded to be controlled by two types of interaction. First, by specific couplings with the curvature tensor and, second, by a suitable interaction with the electromagnetic field of the $d$-dimensional brane, the latter being dictated by a modification of the recently proposed theory of Quasitopological Electromagnetism. The field equations of the corresponding compactified theories, which are of second order, are solved and general homogenous charged black p-branes are constructed. We explicitly provide homogenous Reissner-Nordström black strings and black p-branes in Einstein-Maxwell theory and homogenous charged Boulware-Deser black p-branes for quadratic and cubic Maxwell-Lovelock gravities.

arXiv commentReferences added. Matches published version

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