Spatiotemporal representation of a two-vortex reconnection as a single rotating vortex

TL;DR

This paper demonstrates that spatiotemporal vortex reconnections can be modeled as single rotating vortices with saddle-shaped geometries in four-dimensional spacetime, unifying reconnection and rotation descriptions.

Contribution

It introduces a novel geometric framework linking vortex reconnections and rotations as saddle-shaped surfaces in spacetime, with applications to electromagnetic fields.

Findings

Reconnections over time are equivalent to spatial rotations of a single line.

Magnetic reconnections can be viewed as a continuous line vector potential rotating in space.

A tilted spatiotemporal optical vortex precesses as two reconnecting vortices.

Abstract

Reconnections and rotations of lines are dual descriptions of the same saddle-shaped spacetime surface. We show that a reconnection between two line occurring over time is a single line that rotates over space progression. Both rotating lines and reconnections possess the same saddle shape sheet geometry in four-dimensional space-time, with different orientations. Cyclic precessing lines occurring over time are arrays of reconnections occurring spatially. We show that a magnetic reconnection occurring over time can be seen as a single continuous line vector potential rotating spatially, where the full evolution traces a saddle shape surface. Finally, we show that a single tilted spatiotemporal optical vortex precesses with spatial progression, and as a result can be seen as two vortices reconnecting. Given the unique spatiotemporal evolution, we also analyzed the relativistic angular momentum of these electromagnetic fields.