Effect of particle spin on trajectory deflection and gravitational lensing

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