Probing the spacetime around Sagittarius A* with radio pulsars

The supermassive black hole at the Galactic center harbors a bound cluster of massive stars that should leave neutron star remnants. Extrapolating from the available data, we estimate that similar to1000 radio pulsars may currently orbit Sgr A* with periods of less than or similar to100 yr. Optimistically, 1-10 of the most luminous of these pulsars may be detectable with current telescopes in periodicity searches at frequencies near 10 GHz, where the effects of interstellar scattering are alleviated. Long-term timing observations of such a pulsar would clearly reveal its Keplerian motion and possibly show the effects of relativistic gravity. We briefly discuss how pulsar timing can be used to study the dynamical and interstellar environment of the central black hole and speculate on the prospects for astrometric observations of an orbiting pulsar.