Connection Theorem in General Relativity

The magnetohydrodynamic theorem on the conservation of the magnetic connections between plasma elements is generalized to relativistic plasmas in curved spacetime. This is achieved by using a generalized Ohm's law that contains Hall effect and electron pressure. The connections between plasma elements, which are established by a covariant connection equation, display a particularly complex structure in curved spacetime. It is shown that these connections can be interpreted in terms of magnetic field lines alone by adopting a 3 þ 1 foliation of spacetime. The consequences of thermal-inertial effects are discussed.This theorem is a key step in order to define magnetic reconnection in high-energy plasmas in General Relativity. Implications are outlined