Dual interpretation of electromagnetic fields in general relativity

Abstract

An energy stress tensor satisfying Rainich's algebraic relations along with a specified metric tensor sometimes admits two alternative Maxwell fields-one with a nonvanishing current vector as source and the other without any source. This paper investigates the conditions for the existence of a source-free interpretation when a "with source" solution with various types of the source current vector (i.e., timelike, null, or spacelike) is known and illustrates the results with some examples. It turns out that in the case of timelike currents, a dual interpretation requires this to be a purely convection current, while in other cases a dual interpretation is possible only if the conductivity is infinite and the "conduction" current is in the direction of the magnetic field.