A third-order approximation for time delay of light propagation in the equatorial plane of Kerr black hole

Abstract

The rotation effect of the gravitational source such as Kerr black hole on the time delay of light propagation has been studied in detail. Although it belongs to the second order, the magnitude of rotation effect may be smaller than that of the third-order effect of mass. In this paper, we calculate the time delay of the propagation of light in the equatorial plane of a Kerr black hole to the third order analytically. It is found that the third-order effect of mass is larger than the rotation effect when the magnitude of impact factor \(|b| < \frac{120-5\pi }{16}\frac{M^3}{J}+M\), with \(M\) and \(J\) being the mass and angular momentum of black hole. The total third-order effects on the time delay are also examined.