Covariant Magnetic Connection Hypersurfaces

TL;DR

This paper generalizes the concept of magnetic connection lines in nonrelativistic MHD to covariant 4-D hypersurfaces in relativistic MHD, accounting for Lorentz transformations and the geometry of electromagnetic fields.

Contribution

It introduces magnetic connection hypersurfaces in 4-D Minkowski space, extending the classical concept to relativistic plasmas with Lorentz covariance.

Findings

Defines 2-D magnetic connection hypersurfaces in 4-D spacetime.

Accounts for loss of simultaneity in different frames.

Provides insights into the geometry of electromagnetic fields when E·B=0.

Abstract

In the single fluid, nonrelativistic, ideal-Magnetohydrodynamic (MHD) plasma description magnetic field lines play a fundamental role by defining dynamically preserved "magnetic connections" between plasma elements. Here we show how the concept of magnetic connection needs to be generalized in the case of a relativistic MHD description where we require covariance under arbitrary Lorentz transformations. This is performed by defining 2-D {\it magnetic connection hypersurfaces} in the 4-D Minkowski space. This generalization accounts for the loss of simultaneity between spatially separated events in different frames and is expected to provide a powerful insight into the 4-D geometry of electromagnetic fields when ${\bf E} \cdot {\bf B} = 0$.