Massless polarized particle and Faraday rotation of light in the Schwarzschild spacetime

Abstract

We present the manifestly covariant Lagrangian of a massless polarized particle, that implies all dynamic and algebraic equations as the conditions of extreme of this variational problem. The model allows for minimal interaction with a gravitational field, leading to the equations, coinciding with Maxwell equations in the geometrical optics approximation. The model allows also a wide class of non minimal interactions, which suggests an alternative way to study the electromagnetic radiation beyond the leading order of geometrical optics. As a specific example, we construct a curvature-dependent interaction in Schwarzschild spacetime, predicting the Faraday rotation of polarization plane, linearly dependent on the wave frequency. As a result, the Schwarzschild spacetime generates a kind of angular rainbow of light: waves of different frequencies, initially linearly-polarized in one direction, acquire different orientations of their polarization planes when propagate along the same ray.

13+7 pages, misprints corrected, minor edits

References in corpus (18)

• Modified geometrical optics of a smoothly inhomogeneous isotropic medium: the anisotropy, Berry phase, and the optical Magnus effect
• Photon wave function
• Spinning test particles in the $\gamma$ spacetime
• Recent progress on the description of relativistic spin: vector model of spinning particle and rotating body with gravimagnetic moment in General Relativity
• Semiclassical Dynamics of Dirac particles interacting with a Static Gravitational Field
• Bounds on spinning particles in their innermost stable circular orbits around rotating braneworld black hole
• Particles as Wilson lines of gravitational field
• Relativistic electron spin dynamics in a strong unipolar laser field
• Non-commutative black holes of various genera in the connection formalism
• Spin dynamics of a millisecond pulsar orbiting closely around a massive black hole
• Maximal efficiency of the collisional Penrose process with spinning particles in Kerr-Sen black hole
• Photon propagation in noncommutative QED with constant external field
• Lorentz transformations, sideways shift and massless spinning particles
• Schwarzschild black hole surrounded by quintessential matter field as an accelerator for spinning particles
• Spin precession as a new window into disformal scalar fields
• Evolution of the electric field along null rays for arbitrary observers and spacetimes
• 5-Dimensional $SO(1,4)$-Invariant Action as an Origin to the Magueijo-Smolin Doubly Special Relativity Proposal
• On the world sheet of anyon in the external electromagnetic field

Cited by in corpus (14)

• Gravitational Faraday effect from on-shell amplitudes
• Gravitational Faraday rotation of gravitational waves by a Kerr black hole
• Quantum corrections to frame-dragging in scattering amplitudes
• Spin wave optics for gravitational waves lensed by a Kerr black hole
• Gravitational analog of Faraday rotation in the magnetized Kerr and Reissner-Nordström spacetimes
• Geodesic motion on the symplectic leaf of $SO(3)$ with distorted $e(3)$ algebra and Liouville integrability of a free rigid body
• Bianchi IX geometry and the Einstein-Maxwell theory
• Gravity-induced birefringence in spherically symmetric spacetimes
• Gravitational orbital Hall effect of vortex light in Lense-Thirring metric
• Poincaré-Chetaev equations in the Dirac's formalism of constrained systems
• The motion of twisted particles in a stellar gravitational field
• Polarization rotation and near-Earth quantum communications
• The precession of particle spin in spherical symmetric spacetimes
• Hidden Momentum and the Absence of the Gravitational Spin Hall Effect in a Uniform Field