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