Propagation time delay and frame dragging effects of lightlike geodesics in the timing of a pulsar orbiting SgrA*

Timing a pulsar in a close orbit around the supermassive black hole SgrA* at the centre of the Milky Way would open the window for an accurate determination of the black hole parameters and for new tests of general relativity and alternative modified gravity theories. 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 of lightlike geodesics in a Kerr space-time, and deduce a relativistic formula for the corresponding frame dragging effect on the arrival time. As an illustration, we treat an edge-on orbit in which the frame dragging effect on the emitted lightlike geodesics is expected to be maximal. We compare our formula for the propagation time delay with Post-Newtonian approaches, and in particular with the frame dragging terms derived in previous works by Wex & Kopeikin and Rafikov & Lai. Our approach correctly identifies the asymmetry of the frame dragging delay with respect to superior conjunction, avoids singularities in the time delay, and indicates that in the Post-Newtonian approach frame dragging effects on the lightlike pulses are generally slightly overestimated.

Automated summary

This study discusses the timing of a pulsar in a close orbit around the supermassive black hole SgrA* at the center of the Milky Way, aiming to accurately determine the black hole parameters and test general relativity and alternative gravity theories. The research shows that the propagation delay of pulses in the gravitational field of the black hole must be taken into account due to the extreme mass ratio between the pulsar and the supermassive black hole. By deriving an exact analytical formula for the propagation delay in Kerr spacetime and deducing a relativistic formula for the frame dragging effect on arrival time, the study provides insights into the asymmetry and accuracy of frame dragging effects in the Post-Newtonian approach.