Towards a novel no-hair theorem for black holes

Thomas Hertog
Phys. Rev. D 74, 084008 – Published 6 October 2006

Abstract

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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  • Received 17 August 2006

DOI:https://doi.org/10.1103/PhysRevD.74.084008

©2006 American Physical Society

Authors & Affiliations

Thomas Hertog*

  • Theory Division, CERN, CH-1211 Geneva 23, Switzerland and APC, 11 Place Marcelin Berthelot, 75005 Paris, France†

  • *Electronic address: Thomas.Hertog@cern.ch
  • UMR 7164 (CNRS, Université Paris 7, CEA, Observatoire de Paris)

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Issue

Vol. 74, Iss. 8 — 15 October 2006

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