Spherically symmetric static problem of General Relativity for a continuum

The paper is an analytical review devoted to the spherically symmetric problem of General Relativity (GR). This problem is of special interest in GR, since it is reducible to ordinary differential equations that allow an analytical solution, used to describe cosmological models. The formulation of the mechanics problem associated with the issues of completeness and solvability of GR equations is analyzed. Solutions to the spherically symmetric static problem for a vacuum, ideal fluid, and elastic medium are considered within the framework of classical mechanics, the linearized system of GR equations, the Schwarzschild metric, and a pseudo-Riemannian space of a special type that is flat with respect to spatial coordinates and curved with respect to time.