ABSTRACT: A cornerstone of nonrelativistic ideal magnetohydrodynamics was the realization that two plasma elements connected by a magnetic field line at a given time will remain connected by a magnetic field line at any subsequent time, a result that is generally expressed by saying that the magnetic field lines are “frozen” into the plasma. In highly energetic relativistic plasmas, the distinction between the magnetic and electric fields is frame dependent, and difficulties arise in the generalization of the “frozen-in” theorem to the relativistic regime. The presence of significant gravitational fields, such as the ones characterizing black hole magnetospheres or the early Universe, further complicates the picture. In this talk, I will provide a covariant generalization of the “frozen-in” theorem and show that “generalized magnetic connections” arise in a relativistic plasma. I will discuss how these generalized magnetic connections are destroyed by magnetic reconnection, a fundamental process at work in virtually all magnetized plasmas in space and astrophysics. If time allows, we will also see how magnetic reconnection can serve as a mechanism of energy extraction from rotating black holes, with the potential of spinning down the black hole and powering bright flares.
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