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We review theoretical findings, astrophysical modeling, and current gravitational-wave evidence of hierarchical stellar-mass black-hole mergers. While most of the compact binary mergers detected by LIGO and Virgo are expected to consist of first-generation black holes formed from the collapse of stars, others might instead be of second (or higher) generation, containing the remnants of previous black-hole mergers. Such a subpopulation of hierarchically assembled black holes presents distinctive gravitational-wave signatures, namely higher masses, possibly within the pair-instability mass gap, and dimensionless spins clustered at the characteristic value of $sim$0.7. In order to produce hierarchical mergers, astrophysical environments need to overcome the relativistic recoils imparted to black-hole merger remnants, a condition which prefers hosts with escape speeds $gtrsim$ 100 km/s. Promising locations for efficient production of hierarchical mergers include nuclear star clusters and accretion disks surrounding active galactic nuclei, though environments that are less efficient at retaining merger products such as globular clusters may still contribute significantly to the detectable population of repeated mergers. While GW190521 is the single most promising hierarchical-merger candidate to date, constraints coming from large population analyses are becoming increasingly more powerful.
We investigate the evolution of supermassive binary black holes (BBHs) in galaxies with realistic property distributions and the gravitational-wave (GW) radiation from the cosmic population of these BBHs. We incorporate a comprehensive treatment of t
If a black hole has a low spin value, it must double its mass to reach a high spin parameter. Although this is easily accomplished through mergers or accretion in the case of supermassive black holes in galactic centers, it is impossible for stellar-
The cosmological evolution of the binary black hole (BH) merger rate and the energy density of the gravitational-wave (GW) background are investigated. To evaluate the redshift dependence of the BH formation rate, BHs are assumed to originate from lo
Recent gravitational wave (GW) observations by LIGO/Virgo show evidence for hierarchical mergers, where the merging BHs are the remnants of previous BH merger events. These events may carry important clues about the astrophysical host environments of
We present post-Newtonian $N$-body simulations on mergers of accreting stellar-mass black holes (BHs), where such general relativistic effects as the pericenter shift and gravitational wave (GW) emission are taken into consideration. The attention is