Pulsars at the Galactic Center as probes for theories of gravity

The centre of the Milky Way has been subject of an intense observational program throughout the last thirty years, leading to exhibit the existence of a point source supermassive object named Sagittarius A* (Sgr A*). Thanks to the precise tracking of the motion of stars in its surroundings and the direct imaging of accreting matter in this region, we can now unambiguously identify this object as a supermassive black-hole (SMBH). A promising possibility to enable unparalleled tests of gravity theories and black hole physics is the existence of detectable pulsars in the Galactic Center. While, up to date, no pulsar has been directly observed in orbit around Sgr A* (probably due to scattering effects on the emitted signal), future observing facilities like SKA promise not only to reach this goal, but also to be able to perform timing analysis of such sources. In this talk I will present the work that I have been carrying out to develop a methodology to numerically compute the propagation delay of the light rays emitted by a pulsar orbiting a SMBH in a generic spherically-symmetric space-time.