  In this paper, we explore the signatures of non-rotating and rotating black
hole mergers in the matter-free modified gravity. First, we solve the unstable
circular null orbits and the innermost stable circular timelike orbits via the
geodesic motion. The characteristic quantities of these orbits are
systematically analyzed by varying the black hole spin and the scalar field
parameter of the gravity. Then based on it, we study the ringdown modes from
the light ring/quasinormal modes correspondence. The final spins of the merged
black holes are also estimated with the Buonanno-Kidder-Lehner recipe. Several
black hole merging cases are investigated in detail. All these results show
that the black hole mergers are closely dependent of the scalar field parameter
of the gravity.
