Quasitopological electromagnetism: Reissner-Nordstrom 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 M-D = M-d x K-p, where 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-Nordstrom 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.

Automated summary

In this work, consistent compactifications of Einstein-Maxwell and Einstein-Maxwell-Lovelock theories are provided on direct product spacetimes, with specific flux distribution of p-forms over the internal manifold. The dynamics of the p-forms are controlled by interactions with curvature tensor and electromagnetic field, leading to the construction of homogenously charged black p-branes in the corresponding compactified theories.