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

TL;DR

This paper derives an exact analytical formula for the propagation delay of pulsar signals near a supermassive black hole, comparing it with post-Newtonian approximations to improve timing models for testing gravity.

Contribution

It introduces a new exact delay formula in Schwarzschild spacetime and assesses its accuracy against existing post-Newtonian methods for pulsar timing.

Findings

Exact delay formula outperforms post-Newtonian approximations for edge-on orbits.

Comparison shows the importance of using the exact formula in certain orbital configurations.

Results enhance the precision of pulsar timing near supermassive black holes.

Abstract

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