Light Bending Under General Relativity: A Study of Pulsar–Black Hole Binaries [HBNI Th277]

Abstract

Pulsars are precise cosmic clocks whose timing signals enable stringent tests of general relativity. In binary systems, several propagation delays arise due to orbital motion and gravitational effects, including the Romer delay, Shapiro delay, Einstein delay, and an additional geometric delay caused by gravitational light bending.Light bending also modifies the observed rotational phase of the pulsar, producing longitudinal and latitudinal bending delays and potentially distorting the pulse profile. While earlier studies treated these effects using weak-field approximations, this work adopts a more general approach and refers to them collectively as bending delays.These delays are most significant near superior conjunction, when the pulsar is behind its companion relative to the observer. This study investigates bending effects in pulsar–black hole binaries using realistic system parameters. The results are consistent with existing approximate models, except away from superior conjunction where such approximations fail.Both non-rotating (Schwarzschild) and rotating (Kerr) black hole companions are analyzed. The spin of the black hole has negligible impact on overall bending delays, although small frame-dragging contributions (longitudinal and latitudinal FD delays) of nanosecond order are identified, with discontinuities at specific orbital phases.The dependence of bending delays on parameters such as eccentricity, orbital period, and companion mass is also examined. Pulse profile analysis shows that for stellar-mass black holes, the signal strength increases without significant shape change, especially near superior conjunction.In the strong-field case of supermassive black hole companions, both the shape and strength of the pulse profile change significantly due to the Einstein ring exceeding the beam size, consistent with gravitational lensing theory.Overall, this work highlights the importance of light bending effects in pulsar–black hole binaries for precision timing and strong-field tests of gravity.