No hair for spherical black holes: charged and nonminimally coupled scalar field with self--interaction

Details No hair for spherical black holes: charged and nonminimally coupled scalar field with self--interaction No hair for spherical black holes: charged and nonminimally coupled scalar field with self--interaction

1996-02-28

arxiv.org/abs/gr-qc/9602057v2

Phys.Rev. D54 (1996) 5059-5069

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

30 pages, RevTeX. Sec.IV corrected, simplified and shortened. Corrections to Sec.IIA between Eqs. 2.7 and Eq.2.1. First two pa

Scientific paper

10.1103/PhysRevD.54.5059

We prove three theorems in general relativity which rule out classical scalar hair of static, spherically symmetric, possibly electrically charged black holes. We first generalize Bekenstein's no--hair theorem for a multiplet of minimally coupled real scalar fields with not necessarily quadratic action to the case of a charged black hole. We then use a conformal map of the geometry to convert the problem of a charged (or neutral) black hole with hair in the form of a neutral self--interacting scalar field nonminimally coupled to gravity to the preceding problem, thus establishing a no--hair theorem for the cases with nonminimal coupling parameter $\xi<0$ or $\xi\geq {1\over 2}$. The proof also makes use of a causality requirement on the field configuration. Finally, from the required behavior of the fields at the horizon and infinity we exclude hair of a charged black hole in the form of a charged self--interacting scalar field nonminimally coupled to gravity for any $\xi$.

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