A unified 1PM formula gives the gravitational time delay of relativistic massive and massless particles by a radially moving Schwarzschild lens, matching known light and static limits.
Gravitational lensing by spinning and escaping lenses
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abstract
The effect of currents of mass on bending of light rays is considered in the weak field regime. Following Fermat's principle and the standard theory of gravitational lensing, we derive the gravitomagnetic correction to time delay function and deflection angle caused by a geometrically-thin lens. The cases of both rotating and shifting deflectors are discussed.
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Leading-order gravitational time delay of massive particles by a moving Schwarzschild lens
A unified 1PM formula gives the gravitational time delay of relativistic massive and massless particles by a radially moving Schwarzschild lens, matching known light and static limits.