Merger estimates for rotating Kerr black holes in modified gravity

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.