In this paper we construct new exact solutions in Einstein-Gauss-Bonnet and Lovelock gravity, describing asymptotically flat black strings. The solutions exist also under the inclusion of a cosmological term in the action, and are supported by scalar fields with finite energy density, which are linear along the extended direction and have kinetic terms constructed out from Lovelock tensors. The divergenceless nature of the Lovelock tensors in the kinetic terms ensures that the whole theory is second order. For spherically, hyperbolic and planar symmetric spacetimes on the string, we obtain an effective Wheeler's polynomial which determines the lapse function up to an algebraic equation. For the sake of concreteness, we explicitly show the existence of a family of asymptotically flat black strings in six dimensions, as well as asymptotically AdS 5 × R black string solutions and compute the temperature, mass density and entropy density. We compute the latter by Wald's formula and show that it receives a contribution from the non-minimal kinetic coupling of the matter part, shifting the one-quarter factor coming from the Einstein term, on top of the usual non areal contribution arising from the quadratic Gauss-Bonnet term. Finally, for a special value of the couplings of the theory in six dimensions, we construct strings that contain asymptotically AdS wormholes as well as rotating solutions on the transverse section. By including more scalars the strings can be extended to p-branes, in arbitrary dimensions.

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In this paper, we construct compactifications of generic, higher-curvature Lovelock theories of gravity over direct product spaces of the type M D ¼ M d × S p , with D ¼ d þ p and d ≥ 5, where S p represents an internal, Euclidean manifold of positive constant curvature. We show that this can be accomplished by including suitable nonminimally coupled p − 1-form fields with a field strength proportional to the volume form of the internal space. We provide explicit details of this constructions for the Einstein-Gauss-Bonnet theory in d þ 2 and d þ 3 dimensions by using 1-and 2-form fundamental fields and provide as well the formulas that allow one to construct the same family of compactification in any Lovelock theory from dimension d þ p to dimension d. These fluxed compactifications lead to an effective Lovelock theory on the compactified manifold, allowing one therefore to find, in the Einstein-Gauss-Bonnet case, black holes in the Boulware-Deser family.

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