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Merging compact black-hole (BH) binaries are likely to exist in the nuclear star clusters around supermassive BHs (SMBHs), such as Sgr A$^ast$. 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 orbital axis of the compact binary may experience significant variation due to the frame-dragging effect associated with the spin of the SMBH. The dynamical behavior of the orbital axis can be understood analytically as a resonance phenomenon. We show that rate of change of the binary orbital axis 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 the binary orbital axis, can provide a new probe on the spins of SMBHs.
Gravitational waves can probe the existence of planetary-mass primordial black holes. Considering a mass range of $[10^{-7}-10^{-2}]M_odot$, inspiraling primordial black holes could emit either continuous gravitational waves, quasi-monochromatic sign
In this review, I give a summary of the history of our understanding of gravitational waves and how compact binaries were used to transform their status from mathematical artefact to physical reality. I also describe the types of compact (stellar) bi
Modern astrophysical methods of determination of spins of rotating stellar-mass black hole in close binaries and of supermassive black holes in active galactic nuclei are briefly discussed. Effective spins of coalescing binary black holes derived fro
A measurement of the history of cosmic star formation is central to understand the origin and evolution of galaxies. The measurement is extremely challenging using electromagnetic radiation: significant modeling is required to convert luminosity to m
The transformation of powerful gravitational waves, created by the coalescence of massive black hole binaries, into electromagnetic radiation in external magnetic fields is revisited. In contrast to the previous calculations of the similar effect, we