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

Understand

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.