  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 $(4m+2)+q$.
