2022ApJ...924..127L

Merging compact black hole (BH) binaries are likely to exist in the nuclear star clusters around supermassive BHs (SMBHs), such as Sgr A*. They may also form in the accretion disks of active galactic nuclei. Such compact binaries can emit gravitational waves (GWs) in the low-frequency band (0.001-1 Hz) that are detectable by several planned space-borne GW observatories. We show that the angular momentum vector of the compact binary (L_in) may experience significant variation due to the frame-dragging effect associated with the spin of the SMBH. The dynamical behavior of L_in can be understood analytically as a resonance phenomenon. We show that the rate of change of L_in encodes the information on the spin of the SMBH. Therefore, detecting GWs from compact binaries around SMBHs, particularly the modulation of the waveform associated with the variation of L_in, can provide a new probe of the spins of SMBHs.