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

TL;DR

This paper formulates the initial value problem for black hole perturbations in higher-order scalar-tensor theories and demonstrates the dynamical stability of stealth Schwarzschild solutions against monopole perturbations.

Contribution

It introduces a physically sensible formulation for initial value problems in higher-order scalar-tensor theories and applies it to analyze stability of specific black hole solutions.

Findings

Stealth Schwarzschild solutions are dynamically stable against monopole perturbations.

Late-time oscillations do not resemble standard ringdown in GR.

Monopole perturbations exhibit characteristic curves and static solutions with monopole hair.

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.