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

In this work, we provide consistent compactifications of Einstein-Maxwell and Einstein-Maxwell-Lovelock theories on direct product spacetimes of the form ${\mathcal{M}}_{D}={\mathcal{M}}_{d}\ifmmode\times\else\texttimes\fi{}{\mathcal{K}}^{p}$, where ${\mathcal{K}}^{p}$ is a Euclidean internal manifold of constant curvature. For these compactifications to take place, the distribution of a precise flux of $p$-forms over the internal manifold is required. The dynamics of the $p$-forms are demanded to be controlled by two types of interactions: 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 homogenously charged black $p$-branes are constructed. We explicitly provide homogenous Reissner-Nordstr\"om black strings and black $p$-branes in Einstein-Maxwell theory and homogenously charged Boulware-Deser black $p$-branes for quadratic and cubic Maxwell-Lovelock gravities.