Zero value of the schwarzschild mass for an asymptotically Euclidian system of gravitational waves

A class of asymptotically Euclidian space-times is shown to exist for which the Schwarzschild mass is equal to zero. The coordinate atlases of these space-times satisfy two additional conditions: (partial _kappa ( - gg^{0_k } ) = 0) and (Gamma _{ik}^0 partial _0 g^{ik} - Gamma _{ik}^k partial _0 g^{0_i } = 0) . In aT-orthogonal metricds ² =g ₀₀ dt ² ?g _αβ dx ^α dx ^β these conditions take a simple form: ?₀(detg _αβ ) = 0 and (?₀ g ^αβ )(?₀ g _αβ ) = 0.