Hairy Black-holes in Shift-symmetric Theories

Abstract

Scalar hair of black holes in theories with a shift symmetry are constrained by the no-hair theorem of Hui and Nicolis, assuming spherical symmetry, time-independence of the scalar field and asymptotic flatness. The most studied counterexample is a linear coupling of the scalar with the Gauss-Bonnet invariant. However, in this case the norm of the shift-symmetry current $J^2$ diverges at the horizon casting doubts on whether the solution is physically sound. We show that this is not an issue since $J^2$ is not a scalar quantity, since $J^{\mu }$ is not a diff-invariant current in the presence of Gauss-Bonnet. The same theory can be written in Horndeski form with a non-analytic function $G_5\sim \log X$. In this case the shift-symmetry current is diff-invariant, but contains powers of $X$ in the denominator, so that its divergence at the horizon is again immaterial. We confirm that other hairy solutions in the presence of non-analytic Horndeski functions are pathological, featuring divergences of physical quantities as soon as one departs from time-independence and spherical symmetry. We generalise the no-hair theorem to Beyond Horndeski and DHOST theories, showing that the coupling with Gauss-Bonnet is necessary to have hair.

arXiv comment25 pages

References in corpus (22)

• The galileon as a local modification of gravity
• Generalized G-inflation: Inflation with the most general second-order field equations
• From k-essence to generalised Galileons
• Healthy theories beyond Horndeski
• Degenerate higher derivative theories beyond Horndeski: evading the Ostrogradski instability
• Black hole hair in generalized scalar-tensor gravity
• Exploring gravitational theories beyond Horndeski
• Black hole hair in generalized scalar-tensor gravity: An explicit example
• Degenerate higher order scalar-tensor theories beyond Horndeski up to cubic order
• Degenerate higher order scalar-tensor theories beyond Horndeski and disformal transformations
• A no-hair theorem for the galileon
• Asymptotically flat black holes in Horndeski theory and beyond
• Horndeski: beyond, or not beyond?
• Numerical binary black hole mergers in dynamical Chern-Simons: I. Scalar field
• Challenging the Presence of Scalar Charge and Dipolar Radiation in Binary Pulsars
• Hairy black holes in DHOST theories: Exploring disformal transformation as a solution-generating method
• Hyperbolicity in Spherical Gravitational Collapse in a Horndeski Theory
• Spinning black holes in shift-symmetric Horndeski theory
• Classification of shift-symmetric Horndeski theories and hairy black holes
• Structure of Lanczos-Lovelock Lagrangians in Critical Dimensions
• Black Hole Ringdown as a Probe for Dark Energy
• Generalized 2D dilaton gravity and KGB

Cited by in corpus (23)

• Cosmology with the Laser Interferometer Space Antenna
• Causality Constraints on Black Holes beyond GR
• Effective Field Theory for the Perturbations of a Slowly Rotating Black Hole
• Linear stability of black holes in shift-symmetric Horndeski theories with a time-independent scalar field
• Linear stability of black holes with static scalar hair in full Horndeski theories: generic instabilities and surviving models
• Periodic orbits and gravitational wave radiation in short hair black hole spacetimes for an extreme mass ratio system
• Propagation of scalar and tensor gravitational waves in Horndeski theory
• Scalarization of isolated black holes in scalar Gauss-Bonnet theory in the fixing-the-equations approach
• Scalar-tensor cosmologies without screening
• Scalarization of planar anti de Sitter charged black holes in Einstein-Maxwell-Scalar theory
• Black hole minimum size and scalar charge in shift-symmetric theories
• Singularity resolution and inflation from an infinite tower of regularized curvature corrections
• Nonsingular black holes and spherically symmetric objects in nonlinear electrodynamics with a scalar field
• Stability of neutron stars in Horndeski theories with Gauss-Bonnet couplings
• Symmetric Teleparallel Gauss-Bonnet Gravity and its Extensions
• The cosmic trimmer: Black-hole hair in scalar-Gauss-Bonnet gravity is altered by cosmology
• Two-body problem in theories with kinetic screening
• Angular and radial stabilities of spontaneously scalarized black holes in the presence of scalar-Gauss-Bonnet couplings
• Gravitational wave signatures from dark sector interactions
• Stealth black holes in Aether Scalar Tensor theory
• Shrouded black holes in Einstein-Gauss-Bonnet gravity
• A First-Order Eikonal Framework for Quasinormal Modes, Shadows, Strong Lensing, and Grey-Body Factors in a Scalarized Black-Hole Metric
• Recent Developments in Degenerate Higher Order Scalar Tensor Theories