Generalized Magnetofluid Connections in Curved Spacetime

TL;DR

This paper extends the ideal magnetohydrodynamic theorem to non-ideal relativistic plasmas in curved spacetime, introducing generalized magnetofluid connections that are preserved by plasma dynamics.

Contribution

It formalizes a covariant connection equation incorporating non-ideal effects, unifying electromagnetic and fluid fields into a generalized framework.

Findings

Generalized connections are represented by 2D hypersurfaces linked to an antisymmetric tensor.

These connections are interpreted as generalized magnetofluid vorticity field lines.

The worldsheets of these vorticity lines constrain plasma evolution by preserving connectivity.

Abstract

The ideal magnetohydrodynamic theorem on the conservation of the magnetic connections between plasma elements is extended to non-ideal relativistic plasmas in curved spacetime. The existence of generalized magnetofluid connections that are preserved by the plasma dynamics is formalized by means of a covariant connection equation that includes different non-ideal effects. These generalized connections are constituted by 2-dimensional hypersurfaces, which are linked to an antisymmetric tensor field that unifies the electromagnetic and fluid fields. They can be interpreted in terms of generalized magnetofluid vorticity field lines by considering a 3+1 foliation of spacetime and a time resetting projection that compensates for the loss of simultaneity in different reference frames between spatially separated events. The worldsheets of the generalized magnetofluid vorticity field lines play a fundamental role in the plasma dynamics by prohibiting evolutions that do not preserve the magnetofluid connectivity.