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The characteristics of dust matter in space-time models, admitting theexistence of privilege coordinate systems are given, where the single-particleHamilton-Jacobi equation can be integrated by the method of complete separationof variables. The resulting functional form of the 4-velocity field and energydensity of matter for all types of spaces under consideration is presented.

The space-time models with dust matter that admit separation of variables in Hamilton-Jacobi equations of a test particle