  Most galaxies, including the Milky Way, harbor a central supermassive black
hole (SMBH) weighing millions to billions of solar masses. Surrounding these
SMBHs are dense regions of stars and stellar remnants, such as neutron stars
and black holes. Neutron stars and possibly black holes receive large natal
kicks at birth on the order of hundreds of km s$^{-1}$. The natal kicks that
occur in the vicinity of an SMBH may redistribute the orbital configuration of
the compact objects and alter their underlying density distribution. We model
the effects of natal kicks on a Galactic Center (GC) population of massive
stars and stellar binaries with different initial density distributions. Using
observational constraints from stellar orbits near the GC, we place an upper
limit on the steepness of the initial stellar profile and find it to be
core-like. In addition, we predict that $30-70 \%$ of compact objects become
unbound from the SMBH due to their kicks and will migrate throughout the
galaxy. Different black hole kick prescriptions lead to distinct spatial and
kinematic distributions. We suggest that the Roman Space Telescope may be able
to distinguish between these distributions and thus be able to differentiate
natal kick mechanisms.
