In our previous article (cited as [A]) general requirements were formulated for the solutions of the general-relativity equations that follow from the geometry in the large and from the requirement that the origin be physically realizable [1]. In this article an exact self-consistent equation is described that takes full account of these requirements. The self-consistency is constant with respect to the volume density in the case of a dustlike ball [A17]. Although the self-consistent solution is of measure zero, it enables one to judge the properties of a wide class of solutions as shown by the experience of hydrodynamics.