Towards a Novel no-hair Theorem for Black Holes

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.

25 pages, 11 figures

References in corpus (2)

• Asymptotic behavior and Hamiltonian analysis of anti-de Sitter gravity coupled to scalar fields
• Electrically charged black hole with scalar hair

Cited by in corpus (26)

• Building an AdS/CFT superconductor
• Critical phenomena and thermodynamic geometry of charged Gauss-Bonnet AdS black holes
• Lovelock black holes with a nonlinear Maxwell field
• Gauss-Bonnet Holographic Superconductors
• Some remarks about non-minimally coupled scalar field models
• Static black hole solutions with a self interacting conformally coupled scalar field
• Stars and (Furry) Black Holes in Lorentz Breaking Massive Gravity
• Asymptotically flat black holes sourced by a massless scalar field
• Analytic topological hairy dyonic black holes and thermodynamics
• Incompressible Navier-Stokes Equations from Einstein Gravity with Chern-Simons Term
• Analytic three-dimensional primary hair charged black holes and thermodynamics
• Instability and no-hair paradigm in d-dimensional charged-AdS black holes
• Phase-space of flat Friedmann-Robertson-Walker models with both a scalar field coupled to matter and radiation
• The dynamical behaviour of homogeneous scalar-field spacetimes with general self-interaction potentials
• Dressed black holes in the new tensor-vector-scalar theory
• Qualitative analysis and characterization of two cosmologies including scalar fields
• Black-Hole Solutions to Einstein's Equations in the Presence of Matter and Modifications of Gravitation in Extra Dimensions
• Analytical approach to phase transitions in rotating and non-rotating 2D holographic superconductors
• Anti de Sitter 5D black hole solutions with a self-interacting bulk scalar field: a potential reconstruction approach
• A Holographic model for Non-Relativistic Superconductor
• Noncommutative AdS black hole and the IR holographic superconductor
• Spherically symmetric, static black holes with scalar hair, and naked singularities in nonminimally coupled k-essence
• Compatibility of Einstein minimally coupled self interacting scalar field theory with the solar system tests of gravity
• Black hole solutions of modified gravity theories
• Agujeros Negros con Pelo y Dualidad AdS/CFT
• A new energy bound for Einstein-Scalar theory in AlAdS${}_4$ and holographic bound for deformed CFT${}_3$