On the Most General Static Field in the Relativity Theory

The ten gravitational equations of Einstein's Relativity theory are reducible to a system of only seven equations of a more tractable type when the metric can be written in the form

(1.1)               ds²=V²(x¹, x², x³) dt²-Σgij(x¹, x², x³) dxⁱdx^j.

This case has been studied and called the static case by Prof. Levi-Civita. The space-time then admits a group of isometry defined by the transformation t' = t + constant.