Stiff magnetic field lines. I. A geometrical foundation
Abstract
It is shown that the foliation of a spacetime manifold of codimension 2 provides a basis for the study of the deformation of magnetic field lines. It is found that the fluid flow vector and the curvature vector of a nongeodesic “stiff” magnetic field line are always orthogonal. Further, it is shown that the metric tensor of the 2space orthogonal to the “Maxwellian string” is Lietransported along the magnetic field lines when the magnetic field lines are “stiff.” If there exists a spacelike Killing vector field parallel to the magnetic field, then the magnetic field lines must be “stiff.”
 Publication:

General Relativity and Gravitation
 Pub Date:
 March 1981
 DOI:
 10.1007/BF00758549
 Bibcode:
 1981GReGr..13..217P