Merger estimates for a disformal Kerr black hole in quadratic degenerate higher-order scalar-tensor theories

We investigate the main features of the disformal Kerr black hole merger in quadratic degenerate higher-order scalar-tensor (DHOST) theories. For the ringdown stage of the black hole mergers, we find that, for the prograde orbit, the real part of the quasinormal modes (QNMs) decreases with the increase of the disformal parameter, and imaginary part decreases with it except for the Kerr case for large spin parameter. But for the retrograde orbit, the real part increases with the increase of the disformal parameter and imaginary part always decreases with it. For the approximate final spin, we observe that, regardless of the equal spin merger, unequal spin merger and generic spin configuration merger, the final black hole spin always increases with the increase of the disformal parameter. Our results show that the disformal parameter in the disformal Kerr solution and the MOG parameter in the Kerr-MOG case have obviously different effects on the black hole merger, which suggests the differences of these two spacetime structures.