PROSPECTS FOR PROBING THE SPACETIME OF Sgr A* WITH PULSARS

The discovery of radio pulsars in compact orbits around Sgr A* would allow an unprecedented and detailed investigation of the spacetime of this supermassive black hole. This paper shows that pulsar timing, including that of a single pulsar, has the potential to provide novel tests of general relativity, in particular its cosmic censorship conjecture and no-hair theorem for rotating black holes. These experiments can be performed by timing observations with 100 mu s precision, achievable with the Square Kilometre Array for a normal pulsar at frequency above 15 GHz. Based on the standard pulsar timing technique, we develop a method that allows the determination of the mass, spin, and quadrupole moment of Sgr A*, and provides a consistent covariance analysis of the measurement errors. Furthermore, we test this method in detailed mock data simulations. It seems likely that only for orbital periods below similar to 0.3 yr is there the possibility of having negligible external perturbations. For such orbits, we expect a similar to 10(-3) test of the frame dragging and a similar to 10(-2) test of the no-hair theorem within five years, if Sgr A* is spinning rapidly. Our method is also capable of identifying perturbations caused by distributed mass around Sgr A*, thus providing high confidence in these gravity tests. Our analysis is not affected by uncertainties in our knowledge of the distance to the Galactic center, R-0. A combination of pulsar timing with the astrometric results of stellar orbits would greatly improve the measurement precision of R-0.