Algebraic Formulas for the Computation of the Ricci Tensor

Abstract

Formulas for an easy computation of the Ricci tensor are deduced under the assumption that 7 components of the metric tensor, glk, g44 depend on all four coordinates, g14 = g24 = 0, and g34 = −A(x2, x3)g44. This kind of metric imposes no requirement at all upon the geometrical symmetry in a particular system of comoving coordinates. The formulas can be used without loss of generality also in all other coordinate systems in which the g14 either vanish or depend on the coordinates as expressed above (for instance, in the synchronous reference frame of Landau and Lifshitz).