A no-hair theorem for stars in Horndeski theories

Abstract

We consider a generic scalar-tensor theory involving a shift-symmetric scalar field and minimally coupled matter fields. We prove that the Noether current associated with shift-symmetry vanishes in regular, spherically symmetric and static spacetimes. We use this fact to prove the absence of scalar hair for spherically symmetric and static stars in Horndeski and beyond theories. We carefully detail the validity of this no-hair theorem.

10 pages, 1 figure; important reference added in v2

References in corpus (7)

• Healthy theories beyond Horndeski
• Exploring gravitational theories beyond Horndeski
• Black holes with non-minimal derivative coupling
• Black Holes in Bi-scalar Extensions of Horndeski Theories
• Charged Galileon black holes
• Cosmological self-tuning and local solutions in generalized Horndeski theories
• Self tuning scalar tensor black holes

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