Black holes with gravitational hair in higher dimensions

Abstract

A new class of vacuum black holes for the most general gravity theory leading to second order field equations in the metric in even dimensions is presented. These space-times are locally AdS in the asymptotic region, and are characterized by a continuous parameter that does not enter in the conserve charges, nor it can be reabsorbed by a coordinate transformation: it is therefore a purely gravitational hair. The black holes are constructed as a warped product of a two-dimensional space-time, which resembles the r-t plane of the BTZ black hole, times a warp factor multiplying the metric of a D-2-dimensional Euclidean base manifold, which is restricted by a scalar equation. It is shown that all the Noether charges vanish. Furthermore, this is consistent with the Euclidean action approach: even though the black hole has a finite temperature, both the entropy and the mass vanish. Interesting examples of base manifolds are given in eight dimensions which are products of Thurston geometries, giving then a nontrivial topology to the black hole horizon. The possibility of introducing a torsional hair for these solutions is also discussed.