Covariant Magnetic Connection Hypersurfaces

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 $\mathbf{E}\cdot \mathbf{B}=0$.

10 pages no figures

References in corpus (5)

• Discovery of Powerful Gamma-Ray Flares from the Crab Nebula
• An HLLC Solver for Relativistic Flows -- II. Magnetohydrodynamics
• Generalized Magnetofluid Connections in Relativistic Magnetohydrodynamics
• An Action Principle for Relativistic MHD
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Cited by in corpus (5)

• Magnetic reconnection: from MHD to QED
• Magnetic Connections in Curved Spacetime
• Generalized Magnetofluid Connections in Curved Spacetime
• Lorentz invariant "potential magnetic field" and magnetic flux conservation in an ideal relativistic plasma
• Frozen-In Gravitational Fields