Effect of Particle Spin on Trajectory Deflection and Gravitational Lensing

TL;DR

This paper investigates how the spin of particles influences their deflection and gravitational lensing in stationary, axisymmetric spacetimes, introducing a perturbative method to quantify these effects and potential observational implications.

Contribution

It develops a novel perturbative approach to analyze the impact of particle spin on gravitational lensing and deflection in complex spacetimes, including finite distance effects.

Findings

Spin parallel or antiparallel to orbital angular momentum alters deflection angles.

Spin affects apparent angles and time delays in gravitational lensing.

Time delays between signals with opposite spins relate to the spin-to-mass ratio, useful for neutrino studies.

Abstract

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.