Abstract
Symmetries of energy–momentum tensors 𝒯 in a Riemannian space–time are defined by infinitesimal mappings x̄i =xi+ξi(x) δa where the mapping vector ξi is determined by the symmetry condition ℒξ(gw/2𝒯) =0, (gw/2𝒯) is a relative tensor of weight w, g≡ absolute value of the metrical determinant, and ℒξ is the Lie derivative with respect to the vector ξi). The existence of such symmetry vectors ξi leads to concomitant conservation laws in the form of conserved vector currents Ji for both special and general relativity. The currents Ji will be explicit functions of the energy momentum tensor 𝒯 and the symmetry vector ξi. 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.
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