Relativistic propagation and frame dragging time delay in the timing of a pulsar orbiting the supermassive black hole SgrA*

TL;DR

This paper derives an exact analytical formula for pulse propagation delay and frame dragging effects in pulsar timing around SgrA*, improving accuracy over previous Post-Newtonian methods and aiding tests of gravity theories.

Contribution

It introduces a new exact analytical approach for relativistic pulse delay and frame dragging in Kerr spacetime, surpassing prior approximations.

Findings

The formula correctly captures delay asymmetry and avoids singularities.

Frame dragging effects are slightly overestimated by Post-Newtonian methods.

The approach enhances precision in pulsar timing near supermassive black holes.

Abstract

Timing a pulsar in a close orbit around the supermassive black hole SgrA* at the center 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 in a Kerr spacetime and deduce a relativistic formula for the frame dragging effect on the arrival time. As an illustration, we treat an edge-on orbit in which the frame dragging effect 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 are generally slightly overestimated.