  Pulsars, if existing and detectable in the immediate vicinity of the massive
black hole (MBH) in the Galactic center (GC), may be used as a superb tool to
probe both the environment and the metric of the central MBH. The recent
discovery of a magnetized pulsar in the GC suggests that many more pulsars
should exist near the MBH. In this paper, we estimate the number and the
orbital distribution of pulsars in the vicinity of the MBH in the GC by
assuming that the pulsar progenitors, similar to the GC S-stars, were captured
to orbits tightly bound to the MBH through the tidal breakup of stellar
binaries. We use the current observations on both the GC S-stars and the
hypervelocity stars to calibrate the injection rate(s) of and the dynamical
model(s) for the stellar binaries. By including the relaxation processes,
supernova kicks, and gravitational wave radiation in our simulations, we
estimate that ~97-190 (9-14) pulsars may presently orbit the central MBH with
semimajor axes <=4000AU (<=1000AU), which is compatible with the current
observational constraints on the number of the GC pulsars. The semimajor axis
and the pericenter distance of the pulsar closest to the central MBH are
probably in the range of ~120-460AU and ~2-230AU, respectively. Future
telescopes, such as the SKA, may be able to detect a significant number of
pulsars with semimajor axis smaller than a few thousand AU in the GC. Long-term
monitoring of these pulsars would be helpful in constraining both the
environment and the metric of the central MBH. Our preferred model also results
in about ten hyperfast pulsars with velocity >~1500km/s moving away from the
Milky Way.
