Towards a Novel no-hair Theorem for Black Holes

Details Towards a Novel no-hair Theorem for Black Holes Towards a Novel no-hair Theorem for Black Holes

2006-08-16

arxiv.org/abs/gr-qc/0608075v1

Phys.Rev.D74:084008,2006

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

25 pages, 11 figures

Scientific paper

10.1103/PhysRevD.74.084008

We provide strong numerical evidence for a new no-scalar-hair theorem for black holes in general relativity, which rules out spherical scalar hair of static four dimensional black holes if the scalar field theory, when coupled to gravity, satisfies the Positive Energy Theorem. This sheds light on the no-scalar-hair conjecture for Calabi-Yau compactifications of string theory, where the effective potential typically has negative regions but where supersymmetry ensures the total energy is always positive. In theories where the scalar tends to a negative local maximum of the potential at infinity, we find the no-scalar-hair theorem holds provided the asymptotic conditions are invariant under the full anti-de Sitter symmetry group.

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