Black holes with gravitational hair in higher dimensions

TL;DR

This paper introduces a new class of higher-dimensional vacuum black holes with gravitational hair, characterized by a continuous parameter, vanishing charges, and unique topologies, expanding the understanding of black hole solutions in advanced gravity theories.

Contribution

It presents the first explicit construction of higher-dimensional black holes with gravitational hair that do not affect conserved charges, broadening the landscape of black hole solutions in second-order gravity theories.

Findings

All Noether charges vanish for these black holes.

Entropy and mass are zero despite finite temperature.

Examples include topologically nontrivial horizons in eight 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.