Time delay due to spin and gravitational lensing

We show that when different light beams are deflected by the mass of a rotating object, with angular momentum J, and then, by gravitational lensing, observed at a far point as different images of the same source with different angular positions, there may be a significant time delay between the different images due to the spin of the deflecting body; this effect may be large enough to be detected at Earth. In addition to the time delay due to spin, there is a deflection of the path of electromagnetic waves due to spin. Thus, we show that with three images of the source we may, in principle, have enough information to solve for mass, spin, quadrupole moment and orientation of the deflecting rotating body. We then analyse this effect for the well-known Einstein cross by assuming a simple model for rotation and shape of the central object; we find that the time delay due to spin is appreciable for the different images. In conclusion, this phenomenon should be taken into account in the modelling of the time delay of different images from gravitational lensing and might be measurable in some gravitational lensing images.