No hair theorems for positive Λ

Abstract

We extend all known black hole no-hair theorems to space-times endowed with a positive cosmological constant $\Lambda .$ Specifically, we prove that static spherical black holes with $\Lambda >0$ cannot support scalar fields in convex potentials and Proca-massive vector fields in the region between black hole and cosmic horizons. We also demonstrate the existence of at least one type of quantum hair, and of exactly one charged solution for the Abelian Higgs model. Our method of proof can be applied to investigate other types of quantum or topological hair on black holes in the presence of a positive $\Lambda .$

8pp. v2: added references; comment regarding phantom field, comment that spherical symmetry is not crucial for most of the proof; version published in PRL(name changed in journal)

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• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
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• Dark energy and the generalized second law
• Quantum Hair on Black Holes
• de Sitter black hole with a conformally coupled scalar field in four dimensions
• Abelian Higgs Hair for Black Holes
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• A Cosmological No-Hair Theorem
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Cited by in corpus (26)

• Novel Black-Hole Solutions in Einstein-Scalar-Gauss-Bonnet Theories with a Cosmological Constant
• Constraining some Horndeski gravity theories
• Black hole spontaneous scalarisation with a positive cosmological constant
• Large and Ultra-compact Gauss-Bonnet Black Holes with a Self-interacting Scalar Field
• Thermodynamical properties of hairy black holes in n spacetimes dimensions
• Can Brans-Dicke theory with $\Lambda >0$ describe stars?
• Black Holes and Boson Stars with One Killing Field in Arbitrary Odd Dimensions
• No-hair theorems for a static and stationary reflecting star
• Quantum tunneling from rotating black holes with scalar hair in three dimensions
• No hair theorems for stationary axisymmetric black holes
• On the equivalence of Jordan and Einstein frames in scale-invariant gravity
• Constraints on the symmetry noninheriting scalar black hole hair
• Spontaneous Lorentz violation and asymptotic flatness
• Effect of a positive cosmological constant on cosmic strings
• Late-time evolution of Dirac field around Schwarzschild-quintessence black hole
• Scalarization-like mechanism through spacetime anisotropic scaling symmetry
• Higher-dimensional solitons and black holes with a non-minimally coupled scalar field
• Exact black-hole formation with a conformally coupled scalar field in three dimensions
• Hairy black holes in N=2 gauged supergravity
• On symmetry inheritance of nonminimally coupled scalar fields
• Static de-Sitter Black Holes Abhor Charged Scalar Hair
• Note on black hole no hair theorems for massive forms and spin-1/2 fields
• Massive spin-2 and spin-1/2 no hair theorems for stationary axisymmetric black holes
• No-Go Theorems for Hairy Black Holes in Scalar- or Vector-Tensor-Gauss-Bonnet Theory
• On instabilities of stationary scalar field configurations supported by reflecting compact stars
• Exact Solutions and Black Hole Stability in Higher Dimensional Supergravity Theories