Non-linear electrodynamicsin the Newman-Penrose formalism

An approach to non-linear electrodynamics by means of the spin-coefficient formalism of Newman and Penrose is presented. The field equations are rewritten in the Newman-Penrose form, and their spherically symmetric solutions are discussed. An approximation procedure, suitable for treating radiation problems in non-linear electrodynamics, is then suggested on the basis of an analysis of the Maxwell electrodynamics with sources. Conserved quantities, analogous to those discovered by Newman and Penrose in Maxwell's and Einstein's theories are found for a large class of non-linear theories of electrodynamics. Their number depends on the choice of a particular theory - it is greater than, or equal to 16 for theories satisfying the correspondence principle with Maxwell's theory. (author)