Stationary Black Holes with Time-Dependent Scalar Fields

Abstract

It has been well known since the 1970s that stationary black holes do not generically support scalar hair. Most of the no-hair theorems which support this depend crucially upon the assumption that the scalar field has no time dependence. Here we fill in this omission by ruling out the existence of stationary black hole solutions even when the scalar field may have time dependence. Our proof is fairly general, and in particular applies to non-canonical scalar fields and certain non-asymptotically flat spacetimes. It also does not rely upon the spacetime being a black hole.

arXiv comment5 pages. v2: typos corrected, references added and some additional comments. Matches published version

References in corpus (19)

• A Dynamical Solution to the Problem of a Small Cosmological Constant and Late-time Cosmic Acceleration
• k-Inflation
• The galileon as a local modification of gravity
• Essentials of k-essence
• Kinetically Driven Quintessence
• Kerr black holes with scalar hair
• Stationary Black Holes: Uniqueness and Beyond
• Black hole hair in generalized scalar-tensor gravity
• Black holes in scalar-tensor gravity
• Dressing a black hole with a time-dependent Galileon
• A no-hair theorem for the galileon
• A Higher Dimensional Stationary Rotating Black Hole Must be Axisymmetric
• Dynamics of $k$-essence
• Haloes of k-Essence
• Exact black hole solutions in shift symmetric scalar-tensor theories
• Scalar mesostatic field with regard for gravitational effects
• Black Holes: Classical Properties, Thermodynamics and Heuristic Quantization
• Non-Existence of Black Holes with Non-Canonical Scalar Fields
• No-scalar hair conjecture in asymptotic de-Sitter spacetime

Cited by in corpus (40)

• Testing General Relativity with Present and Future Astrophysical Observations
• Black holes as particle detectors: evolution of superradiant instabilities
• Testing the black hole "no-hair" hypothesis
• Black Hole Based Tests of General Relativity
• Black Holes and Scalar Fields
• Scalarized black holes in the presence of the coupling to Gauss-Bonnet gravity
• Kerr black holes with self-interacting scalar hair: hairier but not heavier
• Challenging the Presence of Scalar Charge and Dipolar Radiation in Binary Pulsars
• Sgr A* and General Relativity
• Testing the No-Hair Theorem with Observations of Black Holes in the Electromagnetic Spectrum
• Charged Galileon black holes
• Instability of hairy black holes in shift-symmetric Horndeski theories
• Linear perturbation analysis of hairy black holes in shift-symmetric Horndeski theories: Odd-parity perturbations
• Black hole solutions in scalar-tensor symmetric teleparallel gravity
• No-hair theorems for a static and stationary reflecting star
• Scalarized Black Holes in Teleparallel Gravity
• Black holes with a nonconstant kinetic term in degenerate higher-order scalar tensor theories
• Scalar clouds in charged stringy black hole-mirror system
• On Lovelock galileons and black holes
• Symmetry inheritance of scalar fields
• Black hole hairs in scalar-tensor gravity and the lack thereof
• Self Tuning Scalar Fields in Spherically Symmetric Spacetimes
• Wave propagation and shock formation in the most general scalar-tensor theories
• Virial identities in relativistic gravity: 1D effective actions and the role of boundary terms
• Robinson-Trautman solution with scalar hair
• Symmetry of Brans-Dicke gravity as a novel solution-generating technique
• Warped-AdS3 black holes with scalar halo
• Instability of scalarized compact objects in Einstein-scalar-Gauss-Bonnet theories
• Constraints on the symmetry noninheriting scalar black hole hair
• Compact astrophysical objects in modified gravity
• Does three dimensional electromagnetic field inherit the spacetime symmetries?
• Analytical external spherical solutions in entangled relativity
• Black holes in the quadratic-order extended vector-tensor theories
• No-hair theorems for non-canonical self-gravitating static multiple scalar fields
• Hybrid imploding scalar and ads spacetime
• Stationary spacetimes with time-dependent real scalar fields
• Time-Dependent Scalar Fields in Modified Gravities in a Stationary Spacetime
• K-nonizing
• Stealth black hole solutions in higher-order Maxwell-Einstein theories
• Fundamental fields around compact objects: Massive spin-2 fields, Superradiant instabilities and Stars with dark matter cores