Time Delay Of Light In Gravitational Field

Time delay of electromagnetic wave which is a canonical examination of general relativity has been studied in detail, however, the calculation about time delay in the harmonic coordinates and the third-order effects in B-L coordinates for the Kerr field has never been studied.Firstly, we calculate the second-order time delay of light when it propagates from the source point1to the observation point2under the assumption of the weak Schwarzschild field in the standard, harmonic and isotropic coordinates of respectively. For the second-order time delay, the calculation results in terms of impact factor b, are the same in the harmonic and isotropic coordinates, but deviate from the one in the standard coordinates with magnitude of2m. Here m is the mass of gravitational source. If we want the accuracy of the time delay caused by the Sun to be smaller than10//sec, the zero order of the propagating time from point1to point2must be accurate to1.5km(≈1.02mo). Here mo denotes the Sun’s mass. Therefore it is necessary to specify the choice of coordinates in the experiments.Secondly, we calculate the second-order time delay of light under the assumption of the weak Kerr field in the harmonic coordinates, when it propagates from the source point1to the observation point2in the equatorial plane, and then compare the calculation result with the one in the B-L coordinate. We find that the effect caused by the difference of coordinates is much larger than the rotation one. It suggests that the coordinate must be specified when the rotation effect is considered in the calculation of time delay in the Kerr field.Finally, we calculate the time delay of the propagation of light within the equatorial plane of 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|<(120-5π)m3/6J+m with m and J being the mass and angular momentum of the black hole.