Magnetic Connections in Curved Spacetime

TL;DR

This paper extends the ideal MHD theorem to relativistic plasmas in curved spacetime, revealing complex connection structures that can be interpreted through a 3+1 spacetime foliation.

Contribution

It generalizes the conservation of magnetic connections to curved spacetime and provides a covariant connection equation for plasma elements.

Findings

Connections are complex in curved spacetime

Connections can be interpreted via magnetic field lines with 3+1 foliation

The covariant connection equation describes plasma element relationships

Abstract

The ideal MHD theorem on the conservation of the magnetic connections between plasma elements is generalized to relativistic plasmas in curved spacetime. The connections between plasma elements, which are established by a covariant connection equation, display a particularly complex structure in curved spacetime. Nevertheless, it is shown that these connections can be interpreted in terms of magnetic field lines alone by adopting a $3+1$ foliation of spacetime.