Searching for non-minimally coupled scalar hairs

Abstract

In this work we study the asymptotically flat, static, and spherically symmetric black-hole solutions of the theory described by the action $$S=\int d^{n}x\sqrt{-g}\left\{\left(1-\xi {\varphi }^2\right)R-g^{\mu \nu }{\partial }_{\mu }\varphi {\partial }_{\nu }\varphi \right\},$$ with $n>3$ and arbitrary $\xi$. We demonstrate the absence of scalar hairs for $\xi <0$. For $\xi >{\xi }_c=\frac{n-2}{4(n-1)}$, we show that there is no scalar hair obeying $|\varphi (r)|<1/\sqrt{\xi }$ or $|\varphi (r)|>1/\sqrt{\xi }$. For $0<\xi <{\xi }_c$, we prove the absence of scalar hairs such that $|\varphi (r)|<1/\sqrt{\xi }$ or $\frac{1}{\xi }<{\varphi }^2(r)<\frac{{\xi }_c}{\xi ({\xi }_c-\xi )}$.

Revtex, 10 pages

Cited by in corpus (23)

• Exact black hole solution with a minimally coupled scalar field
• Topological black holes dressed with a conformally coupled scalar field and electric charge
• The Cauchy problem of scalar-tensor theories of gravity
• Scalar hairy black holes and solitons in asymptotically flat spacetimes
• On the existence of conformally coupled scalar field hair for black holes in (anti-)de Sitter space
• Electrically charged black hole with scalar hair
• Note on Scalar Fields Non-Minimally Coupled to (2+1)-Gravity
• The vacuum revealed: the final state of vacuum instabilities in compact stars
• Dressing a black hole with non-minimally coupled scalar field hair
• Black hole solutions in scalar-tensor symmetric teleparallel gravity
• Static black hole solutions with a self interacting conformally coupled scalar field
• No nonminimally coupled massless scalar hair for spherically symmetric neutral reflecting stars
• Scalarized Black Holes in Teleparallel Gravity
• No nonminimally coupled massless scalar hair for spherically symmetric neutral black holes
• "No-Scalar-Hair" Theorems for Nonminimally Coupled Fields with Quartic Self-Interaction
• On uniqueness of static spacetimes with non-trivial conformal scalar field
• Constraints on the symmetry noninheriting scalar black hole hair
• Field redefinitions, Weyl invariance, and nature of mavericks
• Higher-dimensional solitons and black holes with a non-minimally coupled scalar field
• High precision numerical sequences of rotating hairy black holes
• No minimally coupled scalar black hole hair in Lanczos-Lovelock gravity
• On symmetry inheritance of nonminimally coupled scalar fields
• No scalar hair theorem for neutral Neumann stars: static massive scalar fields nonminimally coupled to gravity