  Radio timing observations of a millisecond pulsar in orbit around the
Galactic centre black hole (BH) or a BH at the centre of globular clusters
could answer foundational questions in astrophysics and fundamental physics.
Pulsar radio astronomy typically employs the post-Keplerian approximation to
determine the system parameters. However, in the strong gravitational field
around the central BH, higher order relativistic effects may become important.
We compare the pulsar timing delays given by the post-Keplerian approximation
with those given by a relativistic timing model. We find significant
discrepancies between the solutions derived for the Einstein delay and the
propagation delay (i.e. Roemer and Sharpiro delay) compared to the fully
relativistic solutions. Correcting for these higher order relativistic effects
is essential in order to construct accurate radio timing models for pulsar
systems at the Galactic centre and the centre of globular clusters and
informing issues related to their detection.
