Axial perturbations of black holes in scalar-tensor gravity: near-horizon behaviour
arXiv:2304.03055 · doi:10.1088/1475-7516/2023/11/040
Abstract
We consider axial (or odd-parity) perturbations of non-spinning hairy black holes (BH) in shift-symmetric DHOST (Degenerate Higher-Order Scalar-Tensor) theories, including terms quartic and cubic in second derivatives of the scalar field. We give a new formulation of the effective metric in which axial perturbations propagate as in general relativity. We then introduce a generic parametrization of the effective metric in the vicinity of the background BH horizon. Writing the dynamics of the perturbations in terms of a Schrödinger-like operator, we discuss in which cases the operator is (essentially) self-adjoint, thus leading to an unambiguous time evolution, according to the choice of parameters characterizing the near-horizon effective metric. This is in particular useful to investigate the stability of the perturbations. We finally illustrate our general analysis with two examples of BH solutions.
24 pages, 3 appendices
References in corpus (32)
- Horndeski theory and beyond: a review
- Degenerate higher order scalar-tensor theories beyond Horndeski up to cubic order
- Horndeski Gravity as Limit of Gauss-Bonnet
- On Taking the limit of Gauss-Bonnet Gravity: Theory and Solutions
- Pseudospectrum and black hole quasi-normal mode (in)stability
- Gravitational wave signatures of black hole quasi-normal mode instability
- Perturbations of Stealth Black Holes in DHOST Theories
- Exact black hole solutions in shift-symmetric quadratic degenerate higher-order scalar-tensor theories
- Linear stability analysis of hairy black holes in quadratic degenerate higher-order scalar-tensor theories: Odd-parity perturbations
- Hairy black holes in DHOST theories: Exploring disformal transformation as a solution-generating method
- Weakly-coupled stealth solution in scordatura degenerate theory
- General Relativity solutions with stealth scalar hair in quadratic higher-order scalar-tensor theories
- Existence and Instability of Novel Hairy Black Holes in Shift-symmetric Horndeski Theories
- Invertible disformal transformations with higher derivatives
- Black hole perturbations in DHOST theories: Master variables, gradient instability, and strong coupling
- Linear perturbation analysis of hairy black holes in shift-symmetric Horndeski theories: Odd-parity perturbations
- Effective Field Theory for the Perturbations of a Slowly Rotating Black Hole
- Generalized disformal Horndeski theories: cosmological perturbations and consistent matter coupling
- Effective Field Theory of Black Hole Perturbations with Timelike Scalar Profile: Formulation
- Generalized Regge-Wheeler Equation from Effective Field Theory of Black Hole Perturbations with a Timelike Scalar Profile
- Perturbations and quasi-normal modes of black holes with time-dependent scalar hair in shift-symmetric scalar-tensor theories
- Relativistic star perturbations in Horndeski theories with a gauge-ready formulation
- Black holes with a nonconstant kinetic term in degenerate higher-order scalar tensor theories
- 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
- Stability of black holes with non-minimally coupled scalar hair to the Einstein tensor
- Asymptotics of linear differential systems and application to quasi-normal modes of nonrotating black holes
- Consistency of higher derivative couplings to matter fields in scalar-tensor gravity
- Stability of Hairy Black Holes in Shift-Symmetric Scalar-Tensor Theories via the Effective Field Theory Approach
- Linear perturbations of Einstein-Gauss-Bonnet black holes
- On the effective metric of axial black hole perturbations in DHOST gravity
- Black hole perturbations in higher-order scalar-tensor theories: initial value problem and dynamical stability