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Black hole hair in generalized scalar-tensor gravity · Around

2013

Black hole hair in generalized scalar-tensor gravity

Sotiriou, Thomas P., Zhou, Shuang-Yong

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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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