Timing Gravity with Pulsars in the Strong Field
We propose a novel approach for the timing of pulsars orbiting a supermassive black hole, which implements the fully relativistic calculations of the photon travel time into a robust timing model. We generate realistic mock catalogues of pulsar times-of-arrival for several putative pulsars on tight orbits around the Galactic Center supermassive black hole, Sagittarius A* (Sgr A*). Then, we perform a proof-of-concept sensitivity analysis to forecast the accuracy that future observational facilities, like the Squared Kilometer Array, will achieve in the characterization of the parameters of our timing model. Our analysis shows how the observation of pulsars at the Galactic Center will open an incredibly promising avenue for the characterization of the physical properties of Sgr A*, which can improve by at least three orders of magnitude the current constraints on the black hole's mass achieved with the S-stars and event-horizon scale observations.