Birth, life, and death of black hole binaries around supermassive black
  holes: dynamical evolution of gravitational wave sources
  In this paper, we explore the mechanisms that regulate the formation and
evolution of stellar black hole binaries (BHBs) around supermassive black holes
(SMBHs). We show that dynamical interactions can efficiently drive "in-situ"
BHB formation if the SMBH is surrounded by a massive nuclear cluster (NC),
while orbitally segregated star clusters can replenish the BHB reservoir in
SMBH-dominated nuclei. We discuss how the combined action of stellar hardening
and mass segregation sculpts the BHB orbital properties. We use direct N-body
simulations including post-Newtonian corrections up to 2.5 order to study the
BHB-SMBH interplay, showing that the Kozai-Lidov mechanism plays a crucial role
in shortening binaries lifetime. We find that the merging probability weakly
depends on the SMBH mass in the $10^6-10^9{\rm ~M}_\odot$ mass range, leading
to a merger rate $\Gamma \simeq 3-8$ yr$^{-1}$ Gpc$^{-3}$ at redshift zero.
Nearly $40\%$ of the mergers have masses in the "BH mass gap", $50-140{\rm
~M}_\odot$, thus indicating that galactic nuclei are ideal places to form BHs
in this mass range. We argue that gravitational wave (GW) sources with
components mass $m_1>40{\rm ~M}_\odot$ and $m_2<30{\rm ~M}_\odot$ would
represent a strong indicator of a galactic nuclei origin. The majority of these
mergers could be multiband GW sources in the local Universe: nearly $40\%$
might be seen by LISA as eccentric sources and, a few years later, as circular
sources by LIGO and the Einstein Telescope, making decihertz observatories like
DECIGO unique instruments to bridge the observations during the binary
inspiral.
