Testing gravity of a disformal Kerr black hole in quadratic degenerate higher-order scalar-tensor theories by quasi-periodic oscillations

By using the relativistic precession model, we have studied frequencies of quasi-periodic oscillations in spacetime a disformal Kerr black hole. This hole owns an extra parameter and belongs to class non-stealth solutions quadratic degenerate higher-order scalar-tensor (DHOST) theories. Our result shows that only periastron frequency is related parameter, while azimuthal nodal are identical with those usual general relativity. Combing observation data GRO J1655-40, fit parameters hole, find $\alpha$ almost negative range $1 \sigma$, which implies favored by J1655-40.