Spinoptics in the Schwarzschild spacetime

TL;DR

This paper analyzes spinoptics in Schwarzschild spacetime, solving equations explicitly for null rays, revealing how spin-curvature interaction causes tilting of particle orbits, especially near the photon sphere.

Contribution

It provides explicit solutions to spinoptics equations in Schwarzschild spacetime using symmetries, and quantifies the tilt effect of spin-curvature interaction on null rays.

Findings

Tilt angle increases near the photon sphere at r=3M.

Explicit solutions for electromagnetic and gravitational wave spinoptics.

Main effect is the tilt of asymptotic planes of massless particles.

Abstract

We study spinoptics equations in the Schwarzschild spacetime. We demonstrate that using the explicit and hidden symmetries of this metric one can explicitly solve the equations for complex null tetrad associated with null rays representing photon's and graviton's motion. This allows one to integrate the spinoptics equations both for the electromagnetic and gravitational waves. It is shown that the main effect of the interaction of the spin of these fields with the spacetime curvature is the tilt of the asymptotic planes of the massless particle orbit. The corresponding tilting angle is calculated. It is shown that this angle grows when a null ray passes in the vicinity of the circular null orbit located at $r=3M$.