A second-order approximation to equatorial null geodesics in the Kerr metric - Application to light deflection in eclipsing compact binaries

Goicoechea, L. J.; Mediavilla, E.; Buitrago, J.; Atrio, F.
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Monthly Notices of the Royal Astronomical Society (ISSN 0035-8711), vol. 259, no. 2, p. 281-292.

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We present a second-order analytical expansion of null equatorial geodesics in the Kerr metric. The equations developed are applied to the study of light transit in compact binary systems. We show that the effects arising from path bending have a significant influence on the computed time delays, even at first order of approximation in the Schwarzschild metric, reducing by about 50 percent the lags expected when rectilinear propagation is assumed. We calculate the time delays in the second-order approximation, including the effects derived from light deflection. For systems in which the central object is a rotating black hole, the time lag could even be of the order of minutes. The duration of the eclipse and the amplitude of the lensing effect are also studied and we find a coverage for the lensing effect of almost 180 deg for neutron stars. The influence of the spin of the central object is manifested in the asymmetry of the curve representing time delay versus orbital phase, which is very enhanced in the part affected by lensing.