No hair theorem in quasi-dilaton massive gravity

Abstract

We investigate the static, spherically symmetric black hole solutions in the quasi-dilaton model and its generalizations, which are scalar extended dRGT massive gravity with a shift symmetry. We show that, unlike generic scalar extended massive gravity models, these theories do not admit static, spherically symmetric black hole solutions until the theory parameters in the dRGT potential is fine-tuned. When fine-tuned, the geometry of the static, spherically symmetric black hole is necessarily that of general relativity and the quasi-dilaton field is constant across the spacetime. The fine-tuning and the no hair theorem apply to black holes with flat, anti-de Sitter or de Sitter asymptotics.

11 pages, 1 figure; v2: comments added

References in corpus (6)

• Resummation of Massive Gravity
• Quasi-Dilaton: Theory and Cosmology
• Charged black holes in nonlinear massive gravity
• Rotating black holes in massive gravity
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• Some perspective of thermodynamical and optical properties of black holes in Maxwell-dilaton-dRGT-like massive gravity