On the effective metric of axial black hole perturbations in DHOST gravity
arXiv:2205.07746 · doi:10.1088/1475-7516/2022/08/040
Abstract
We study axial (or odd-parity) perturbations about static and spherically symmetric hairy black hole (BH) solutions in shift-symmetric DHOST (Degenerate Higher-Order Scalar-Tensor) theories. We first extend to the family of DHOST theories the first-order formulation that we recently developed for Horndeski theories. Remarkably, we find that the dynamics of DHOST axial perturbations is equivalent to that of axial perturbations in general relativity (GR) evolving in a, distinct, effective metric. In the particular case of quadratic DHOST theories, this effective metric is derived from the background BH metric via a disformal transformation. We illustrate our general study with three examples of BH solutions. In some so-called stealth solutions, the effective metric is Schwarzschild with a shifted horizon. We also give an example of BH solution for which the effective metric is associated with a naked singularity.
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References in corpus (26)
- Horndeski theory and beyond: a review
- Degenerate higher order scalar-tensor theories beyond Horndeski up to cubic order
- On Taking the limit of Gauss-Bonnet Gravity: Theory and Solutions
- A unifying description of dark energy
- Escaping from the black hole?
- Exact black hole solutions in shift-symmetric quadratic degenerate higher-order scalar-tensor theories
- Cosmological self-tuning and local solutions in generalized Horndeski theories
- Linear stability analysis of hairy black holes in quadratic degenerate higher-order scalar-tensor theories: Odd-parity perturbations
- Weakly-coupled stealth solution in scordatura degenerate theory
- Hairy black holes in DHOST theories: Exploring disformal transformation as a solution-generating method
- Hawking radiation by spherically-symmetric static black holes for all spins: I -- Teukolsky equations and potentials
- Black hole perturbations in DHOST theories: Master variables, gradient instability, and strong coupling
- Black hole perturbations in modified gravity
- Built-in scordatura in U-DHOST
- 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
- Effective Field Theory of Black Hole Perturbations with Timelike Scalar Profile: Formulation
- 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
- Asymptotics of linear differential systems and application to quasi-normal modes of nonrotating black holes
- Stability of black holes with non-minimally coupled scalar hair to the Einstein tensor
- Linear perturbations of Einstein-Gauss-Bonnet black holes
- Quadratic DHOST theories revisited
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- Generalized Regge-Wheeler Equation from Effective Field Theory of Black Hole Perturbations with a Timelike Scalar Profile
- Generalisation of Conformal-Disformal Transformations of the Metric in Scalar-Tensor Theories
- Axial perturbations of hairy black holes in generalised scalar-tensor theories
- An analytic approach to quasinormal modes for coupled linear systems
- Black hole perturbations in spatially covariant gravity with just two tensorial degrees of freedom
- Axial perturbations of black holes in scalar-tensor gravity: near-horizon behaviour
- Universal Horizons without Hypersurface Orthogonality
- Gravitational ringdown in the Minimal Theory of Massive Gravity
- Geometrically Regular Black Holes with Hedgehog Scalar Hair