Perturbative deflection angle for signal with finite distance and general velocities

Abstract

We propose a perturbative method to compute the deflection angle of both null\nand massive particles for source and detector at finite distance. This method\napplies universally to the motion of particles with general velocity in the\nequatorial plane of stationary axisymmetric spacetimes or static spherical\nsymmetric spacetimes that are asymptotically flat. The resultant deflection\nangle automatically arranges into a quasi-inverse series form of the impact\nparameter, with coefficients depending on the metric functions, the signal\nvelocity and the source and detector locations through the apparent angles. In\nthe large impact parameter limit, the series coefficients are reduced to\nrational functions of sine/cosine functions of the zero order apparent angle.\n