title: Black hole hair in generalized scalar-tensor gravity.
abstract: The most general action for a scalar field coupled to gravity that leads to second-order field equations for both the metric and the scalar--Horndeski's theory--is considered, with the extra assumption that the scalar satisfies shift symmetry. We show that in such theories, the scalar field is forced to have a nontrivial configuration in black hole spacetimes, unless one carefully tunes away a linear coupling with the Gauss-Bonnet invariant. Hence, black holes for generic theories in this class will have hair. This contradicts a recent no-hair theorem which seems to have overlooked the presence of this coupling.
authors.affiliation: School of Mathematical Sciences and School of Physics and Astronomy, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom.
authors.forename: Thomas P
authors.initials: TP
authors.lastname: Sotiriou
authors.affiliation: SISSA, Via Bonomea 265, 34136 Trieste, Italy and INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste, Italy.
authors.forename: Shuang-Yong
authors.initials: SY
authors.lastname: Zhou