Time Delay of Pulsar Signals in Astrophysical Black Hole Spacetimes

In this paper, we investigate the fully relativistic time delay of pulsar signals propagating in the vicinity of a rotating black hole and its potential mimickers, including a deformed Kerr black hole and the Janis-Newman-Winicour naked singularity. We aim to compute and compare the pulsar time delays caused by different spacetime geometries to explore possible observational signatures that distinguish between black holes and their alternatives. We begin by solving the equations of motion for null geodesics in these background geometries. Subsequently, we address the emitter-observer problem to compute the time delay of pulsar signals in Kerr, deformed Kerr, and JNW spacetimes. A comparative analysis between Schwarzschild and Kerr black holes allows us to observe the effect of spin on propagation delay in pulsar timing. Further, we examine the impact of the deformation parameter in the deformed Kerr black hole and the influence of the scalar field on the rotating JNW spacetime. Our study considers both direct and indirect photons emitted by a source in the equatorial circular orbit. We find that the variations in the spin parameter show very small but detectable changes when we compare the time delay cases of a Kerr black hole with deformed Kerr and rotating JNW spacetimes. Our pulsar time delay results suggest a potential observable distinguishing feature of these astrophysical black hole geometries which could be useful for the forthcoming observational facilities such as Square Kilometer Array Observatory, Five-hundred-meter Aperture Spherical Telescope and Event Horizon Telescope.