Relativistic Hall Effect

TL;DR

This paper explores the relativistic deformation of quantum and mechanical bodies with intrinsic angular momentum, revealing a relativistic spin Hall effect with implications across scales from particles to black holes.

Contribution

It introduces the relativistic Hall effect, showing how intrinsic angular momentum causes transverse shifts in moving frames, unifying quantum and classical descriptions.

Findings

Centroid shifts depend on angular momentum and differ for geometric and energy centroids.

The effect manifests in quantum vortices and mechanical flywheels.

The phenomenon applies across scales, from particles to black holes.

Abstract

We consider the relativistic deformation of quantum waves and mechanical bodies carrying intrinsic angular momentum (AM). When observed in a moving reference frame, the centroid of the object undergoes an AM-dependent transverse shift. This is the relativistic analogue of the spin Hall effect, which occurs in free space without any external fields. Remarkably, the shifts of the geometric and energy centroids differ by a factor of 2, and both centroids are crucial for the correct Lorentz transformations of the AM tensor. We examine manifestations of the relativistic Hall effect in quantum vortices, and mechanical flywheels, and also discuss various fundamental aspects of this phenomenon. The perfect agreement of quantum and relativistic approaches allows applications at strikingly different scales: from elementary spinning particles, through classical light, to rotating black-holes.