The problem of magnetic topology and reconnection in relativistic systems

It is generally believed that reconnection is an important process in astrophysical plasmas. An essential signature of reconnection processes is the loss of magnetic connection of plasma elements. However the notions of magnetic topology, magnetic connection and magnetic line conservation are not invariant under Lorentz transformantions. Moreover there is no relativistc analogue to magnetic line conservation. This inhibits a straight forward generalization of the usual definition of reconnection for relativistic situations. Instead there exists a relativistic generalization of magnetic flux-conserving plasma flows. This "covariant transport", or "Lie-transport" in Minkowski space, of the electromagnetic field tensor may replace the notion of magnetic line conservation in relativistic situations and hence lead to a covariant definition of reconnection. The invariants of the transport and its relation to different forms of Ohm's law are discussed.