Effect of Particle Spin on Trajectory Deflection and Gravitational Lensing

Spin of a test particle is a fundamental property that can affect its motion in a gravitational field. In this work we consider the effect of particle spin on its deflection angle and gravitational lensing in the equatorial plane of arbitrary stationary and axisymmetric spacetimes. To do this we developed a perturbative method that can be applied to spinning signals with arbitrary asymptotic velocity and takes into account the finite distance effect of the source and the observer. The deflection angle $\Delta\varphi$ and total travel time $\Delta t$ are expressed as (quasi-)power series whose coefficients are polynomials of the asymptotic expansion coefficients of the metric functions. It is found that when the spin and orbital angular momenta are parallel (or antiparallel), the deflection angle is decreased (or increased). Apparent angles $\theta$ of the images in gravitational lensing and their time delays are also solved. In Kerr spacetime, spin affects the apparent angle $\theta_K$ in a way similar to its effect on $\Delta\varphi_K$. The time delay between signals with opposite spins is found to be proportional to the signal spin at leading order. These time delays might be used to constrain the spin to mass ratio of neutrinos.