Quasitopological electromagnetism: Reissner-Nordstr\"om black strings in Einstein and Lovelock gravities

TL;DR

This paper develops consistent compactifications of Einstein-Maxwell and Einstein-Maxwell-Lovelock theories on product spacetimes, introducing a modified quasitopological electromagnetism, and constructs explicit charged black p-brane solutions including Reissner-Nordström black strings.

Contribution

It introduces a new framework for compactifying Einstein-Maxwell-Lovelock theories with fluxes and interactions, leading to explicit solutions of charged black p-branes.

Findings

Derived second-order field equations for compactified theories.

Constructed explicit homogeneous charged black p-brane solutions.

Extended solutions to Einstein-Maxwell 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-Nordstr\"om 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.