No minimally coupled scalar black hole hair in Lanczos–Lovelock gravity

Abstract

We extend here the result of Bekenstein (1995 Phys. Rev. D 51 6608–11, 2000 Cosmology and Gravitation pp 1–85), proving the non-existence of minimally coupled scalar black hole hair in general relativity to the Lanczos–Lovelock gravity in arbitrary dimension with non-negative coupling constants. The only physical requirement on the multiplet of minimally coupled scalar fields is that it fulfills the weak energy condition. We also assume, similarly to Bekenstein, spherical symmetry and asymptotic flatness.