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arxiv: 1312.3622 · v2 · submitted 2013-12-12 · 🌀 gr-qc · hep-th

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Black hole hair in generalized scalar-tensor gravity

Thomas P. Sotiriou , Shuang-Yong Zhou
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classification 🌀 gr-qc hep-th
keywords scalarblackfieldcouplinggravityhairholetheories
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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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