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Nuclear star clusters that surround supermassive black holes (SMBHs) ingalactic nuclei are among the densest systems in the Universe, harbouringmillions of stars and compact objects (COs). Within a few parsecs from theSMBH, stars can form binaries. In this paper, we model the supernova (SN)process of massive binaries that are born in proximity of the SMBH and thatproduce CO binaries. These binaries can later merge via emission ofgravitational waves as a consequence of the Lidov-Kozai mechanism. We study thedynamical evolution of these systems by means of high-precision $N$-bodysimulations, including post-Newtonian (PN) terms up to 2.5PN order. We adoptdifferent prescriptions for the natal velocity kicks imparted during the SNprocesses and find that larger kicks lead to more compact binaries that mergecloser to the SMBH. We also conclude that most of the mergers enter the LIGOband with very high eccentricities. Finally, we compute a merger rate of$0.05$--$0.07\ \mathrm{Gpc}^{-3} \mathrm{yr}^{-1}$, $0.04$--$2\times 10^{-3}\\mathrm{Gpc}^{-3} \mathrm{yr}^{-1}$, $9.6\times 10^{-6}$--$2.7\times 10^{-3}\\mathrm{Gpc}^{-3} \mathrm{yr}^{-1}$ for BH-BH, BH-NS, NS-NS, respectively,smaller than the actual LIGO-Virgo observed rate.

Supernovae in massive binaries and compact object mergers near supermassive black holes