Homogeneous Black Strings in Einstein-Gauss-Bonnet with Horndeski hair and beyond

Understand

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.