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We developed a numerical methodology to compute the fully-relativisticpropagation time of photons emitted by a pulsar in orbit around a massivecompact object, like the supermassive black hole Sagittarius A* in the GalacticCenter, whose gravitational field is described by a generic sphericallysymmetric space-time. Pulsars at the Galactic Center are usually regarded asthe next major precision probe for theories of gravity, filling the currentexperimental gap between horizon-scale gravity tests and those at largerscales. We retain a completely general approach, which allows us to apply ourcode to the Schwarzschild space-time (by which we successfully validate ourmethodology) and to three different well-motivated alternatives to the standardblack hole paradigm. The results of our calculations highlight departuresspanning several orders of magnitudes in timing residuals, that are supposed tobe detectable with future observing facilities like the Square Kilometer Array.

Testing space-time geometries and theories of gravity at the Galactic Center with pulsar's time delay