Testing space–time geometries and theories of gravity at the Galactic centre with pulsar’s time delay

We developed a numerical methodology to compute the fully relativistic propagation time of photons emitted by a pulsar in orbit around a massive compact object, like the supermassive black hole Sagittarius A* in the Galactic centre, whose gravitational field is described by a generic spherically symmetric space–time. Pulsars at the Galactic centre are usually regarded as the next major precision probe for theories of gravity, filling the current experimental gap between horizon-scale gravity tests and those at larger scales. We retain a completely general approach, which allows us to apply our code to the Schwarzschild space–time (by which we successfully validate our methodology) and to three different well-motivated alternatives to the standard black hole paradigm. The results of our calculations highlight departures spanning several orders of magnitudes in timing residuals, that are supposed to be detectable with future observing facilities like the Square Kilometer Array.