Energy--momentum tensor symmetries and concomitant conservation laws. I. Einstein-massless-scalar (meson) field

Symmetries of energy--momentum tensors T in a Riemannian space--time are defined by infinitesimal mappings x-bar/sup i/ =x/sup i/+xi/sup i/(x) deltaa where the mapping vector xi/sup i/ is determined by the symmetry condition L/sub xi/(g/sup w//2T) =0, (g/sup w//2T) is a relative tensor of weight w, gequivalent absolute value of the metrical determinant, and L/sub xi/ is the Lie derivative with respect to the vector xi/sup i/). The existence of such symmetry vectors xi/sup i/ leads to concomitant conservation laws in the form of conserved vector currents J/sup i/ for both special and general relativity. The currents J/sup i/ will be explicit functions of the energy momentum tensor T and the symmetry vector xi/sup i/. The symmetries and conservation laws so obtained will in general differ from the familiar Trautman formulation. The theory is applied to obtain symmetries and conserved currents for a class of conformally flat solutions of the Einstein-massless-scalar (meson) field equations