The preferred null symmetries of a null electromagnetic field interacting with a null free gravitational field

Abstract

The real null vector 1 a of the Newman-Penrose formalism is preferred to correspond to a geometrical symmetry as well as a dynamical symmetry. The 16 types of geometrical symmetries expressed through the vanishing of the Lie derivatives of certain tensor fields with respect to 1 a are examined separately. Two types of dynamical symmetries are imposed simultaneously on 1 a : A null electromagnetic field and a null gravitational field are both chosen to have the same propagation vector 1 a . By adopting freedom conditions on 1 a , it is shown that the symmetries of the null electromagnetic field are shared neither by the free gravitational field nor by the gravitational potentials. In fact the following five preferred null symmmetries are found to be proper: motion, affine collineation, special curvature collineation, curvature collineation, and Ricci collineation. The scalars characterizing the coupled fields are found to be constant with respect to 1 a .