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Black hole hair in generalized scalar-tensor gravity
Thomas P Sotiriou1, Shuang-Yong Zhou2
1School of Mathematical Sciences and School of Physics and Astronomy, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom.
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.
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