Towards an exact approach to pulsar timing

The pulsar timing technique, which compares the observed arrival times of electromagnetic radiation from a pulsar with the predicted arrival times derived from a theoretical model of the pulsar system, is used in pulsar astronomy to infer a multitude of physical information and to constrain possible corrections to General Relativity (GR). The propagation delay is usually computed using formulas based on a post-Newtonian approach, for both the light trajectory and the orbital motion. However, evidence has recently emerged that this approximation may no longer be sufficient when the companion object is a supermassive black hole; deviations from a full GR computation of the propagation delay can reach a few seconds. In this paper, we analyze the case of binary pulsars with a stellar or intermediate black hole companion, whose discovery and timing are key goals of SKA. With a numerical algorithm, we have found that in this case, the full GR value depends only on the semi-major axis of the relative orbit and on the mass of the black hole companion. If the mass of the latter is sufficiently large ($100 M_{\odot}$), the maximum difference between the two approaches is significant ($\sim10^{-7}$ s) even for large binaries ($\sim10^{16}$ cm), and increases up to $\sim 10^{-4}$ s when the mass is $10^5 M_{\odot}$. We also consider relativistic corrections to the orbital motion, and discover that they can strongly affect the value of the propagation delay. We conclude that in the future, post-Newtonian formulas should be replaced with a more accurate approach in these systems, especially in view of future discoveries made by new large telescopes such as SKA.