Exact Hairy Black Holes in Higher-Curvature Scalar--Tensor Gravity

Abstract

We construct exact hairy black holes in Lovelock--Horndeski gravity and establish a relation between horizon topology, scalar hair and covariant charges. Rooted in the dimensional reduction of higher-curvature gravity, this framework connects scalar--tensor dynamics to the low-energy description of heterotic strings. In five dimensions, a single fixed theory admits a continuous planar family and two isolated hyperbolic black holes. The hyperbolic solutions share a locally AdS metric with distinct scalar dressings, while the planar family is Weyl curved and has a freely varying horizon scale. Both branches carry scalar hair regular on the future horizon. The hyperbolic construction extends above four dimensions; compatibility of the displayed planar profile selects five and seven dimensions. Time translations of the scalar act through a global shift, which enters the complete covariant charge balance. Along the planar family, a changing bulk shift-charge density supplies this balance despite zero radial flux and vanishing horizon charge variation. The hyperbolic roots admit no horizon-scale variation at fixed couplings.