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

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