Unified Picture of Electromagnetic and Gravitational Forces in Two-Spinor Language

TL;DR

This paper reformulates the geodesic equation in Weyl two-spinor language, unifying electromagnetic and gravitational forces for a charged spin-1/2 particle, and provides solutions in specific scenarios.

Contribution

It introduces a unified spinor framework combining gravitational and electromagnetic equations of motion for charged particles.

Findings

Unified equations for spacetime trajectories and spin precession.

Solutions for weak gravitational fields in Schwarzschild spacetime.

A novel spinor formulation linking gravity and electromagnetism.

Abstract

The well known Geodesic Equation of General Relativity is newly formulated in Weyl two-spinor language in a convenient way susceptible of being combined with a set of two-spinor equations, equivalent to the Lorentz Force of Electrodynamics, obtained in previous studies. General spinor equations of motion for a test charged spin 1/2 particle in arbitrary electromagnetic and gravitational fields fields are obtained describing not only spacetime trajectories but also spin precession. For the case of the Schwarzschild metric and radial trajectories, spinor equations unifying gravitational and electric forces are obtained and solved for a weak gravitational field (or long distance from the source).