  We propose a dynamical mechanism for capturing stars around a massive black
hole (MBH), which is based on the accumulation there of a very dense cluster of
compact stellar remnants. This study is motivated by the presence of ~10 young
massive stars (M*~3-15 Mo, ~B9V--O8V) less than 0.04 pc from the MBH in the
Galactic center (GC). Their existence in the extreme environment so close to a
MBH is a challenge for theories of star formation and stellar dynamics. We show
that young stars, which formed far from the MBH and were then scattered into
eccentric orbits, repeatedly cross a cluster of stellar black holes (SBHs),
where they may undergo rare direct 3-body exchanges with a MBH-SBH "binary".
The interaction between two objects of similar mass ejects the SBH and captures
the star on a tight orbit around the MBH. Such captures can naturally explain
trends observed in the orbits of the young stars. We derive the capture
cross-section, validate it by Monte-Carlo simulations, and calculate the number
of captured stars in the GC using the currently uncertain estimates of the
numbers of SBHs inside 0.04 pc and of young stars in the inner few pc of the
GC. We find that under favorable conditions 3-body exchange can account for
\~25% of the observed stars, mostly at the fainter end of the observed range.
We discuss additional effects that possibly increase the capture efficiency.
Future observations will establish whether there are enough SBHs and young
stars for exchange captures to singly account for the central young stars. We
estimate that there are also ~35 lower mass stars (M*~1-3 Mo, ~G2V--A0V) inside
0.04 pc similarly captured by exchanges with neutron stars. Ongoing replacement
of compact remnants by main sequence stars may regulate the accumulation of
compact remnants near the MBH.
