Black hole perturbations in higher-order scalar-tensor theories: initial value problem and dynamical stability

Abstract

We propose a physically sensible formulation of initial value problem for black hole perturbations in higher-order scalar-tensor theories. As a first application, we study monopole perturbations around stealth Schwarzschild solutions in a shift- and reflection-symmetric subclass of degenerate higher-order scalar-tensor (DHOST) theories. In particular, we investigate the time evolution of the monopole perturbations by solving a two-dimensional wave equation and analyze the Vishveshwara's classical scattering experiment, i.e., the time evolution of a Gaussian wave packet. As a result, we confirm that stealth Schwarzschild solutions in the DHOST theory are dynamically stable against the monopole perturbations with the wavelength comparable or shorter than the size of the black hole horizon. We also find that the damped oscillations at the late time do not show up unlike the ringdown phase in the standard case of general relativity. Moreover, we investigate the characteristic curves of the monopole perturbations as well as a static spherically symmetric solution with monopole hair.

35 pages, 13 figures, v2: published version in CQG

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Cited by in corpus (7)

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• Generalized Regge-Wheeler Equation from Effective Field Theory of Black Hole Perturbations with a Timelike Scalar Profile
• Tidal Love Numbers from EFT of Black Hole Perturbations with Timelike Scalar Profile
• Black hole ringdown from physically sensible initial value problem in higher-order scalar-tensor theories
• 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
• Recent Developments in Degenerate Higher Order Scalar Tensor Theories