Charged black strings and black branes in Lovelock theories

TL;DR

This paper demonstrates that Lovelock gravity theories allow for new charged black string and brane solutions, overcoming limitations of Einstein-Maxwell theory, and constructs explicit examples in various higher curvature gravity models.

Contribution

It introduces exact charged black brane solutions in Lovelock theories, including cubic and quartic cases, with explicit constructions and symmetry properties.

Findings

Existence of homogeneous charged black strings and branes in Lovelock gravity.

Construction of explicit magnetically charged black branes in cubic Lovelock theory.

Development of dyonic solutions in quartic Lovelock theory.

Abstract

It is well known that the Reissner-Norstrom solution of Einstein-Maxwell theory cannot be cylindrically extended to higher dimension, as with the black hole solutions in vacuum. In this paper we show that this result is circumvented in Lovelock gravity. We prove that the theory containing only the quadratic Lovelock term, the Gauss-Bonnet term, minimally coupled to a $U(1)$ field, admits homogeneous black string and black brane solutions characterized by the mass, charge and volume of the flat directions. We also show that theories containing a single Lovelock term of order $n$ in the Lagrangian coupled to a $(p-1)$-form field admit simple oxidations only when $n$ equals $p$, giving rise to new, exact, charged black branes in higher curvature gravity. For General Relativity this stands for a Lagrangian containing the Einstein-Hilbert term coupled to a massless scalar field, and no-hair theorems in this case forbid the existence of black branes. In all these cases the field equations acquire an invariance under a global scaling scale transformation of the metric. As explicit examples we construct new magnetically charged black branes for cubic Lovelock theory coupled to a Kalb-Ramond field in dimensions $(3m+2)+q$, with $m$ and $q$ integers, and the latter denoting the number of extended flat directions. We also construct dyonic solutions in quartic Lovelock theory in dimension $(4m+2)+q$.