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The observation of a pulsar closely orbiting the galactic center supermassiveblack hole would open the window for an accurate determination of the blackhole parameters and for new tests of General Relativity. An importantrelativistic effect which has to be taken into account in the timing model isthe propagation delay of the pulses in the gravitational field of the blackhole. Due to the extreme mass ratio of the pulsar and the supermassive backhole we use the test particle limit to derive an exact analytical formula forthe propagation delay in a Schwarzschild spacetime. We then compare this resultto the propagation delays derived in the usually employed post-Newtonianapproximation, in particular to the Shapiro delay up to the secondpost-Newtonian order. For edge-on orbits we also consider modifications of theShapiro delay which take the lensing effects into account. Our results are thenused to assess the accuracy of the different orders of the post-Newtonianapproximation of the propagation delay. This comparison indicates that for(nearly) edge-on orbits the new exact delay formula should be used.

The propagation delay in the timing of a pulsar orbiting a supermassive black hole