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

Understand

We extend here the result of Bekenstein [1,2] 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.