Space Inside a Liquid Sphere Transforms into De Sitter Space by Hilbert Radius

Consider space inside a sphere of incompressible liquid, and space surrounding a mass-point. Metrics of the spaces were deduced in 1916 by Karl Schwarzschild. 1) Our calculation shows that a liquid sphere can be in the state of gravitational collapse (g$_{00}$~=~0) only if its mass and radius are close to those of the Universe (M~=~8.7$\times $10$^{55}$~g, a~=~1.3$\times $10$^{28}$~cm). However if the same mass is presented as a mass-point, the radius of collapse r$_{g}$ (Hilbert radius) is many orders lesser: g$_{00}$~=~0 realizes in a mass-point's space by other conditions. 2)~We considered a liquid sphere whose radius meets, formally, the Hilbert radius of a mass-point bearing the same mass: a~=~r$_{g}$, however the liquid sphere is not a collapser (see above). We show that in this case the metric of the liquid sphere's internal space can be represented as de Sitter's space metric, wherein $\lambda $~=~3/a$^{2}$~$>$~0: physical vacuum (due to the $\lambda $-term) is the same as the field of an ideal liquid where $\rho _{0}$~$<$~0 and p~=~-$\rho _{0 }$c$^{2}$~$>$~0 (the mirror world liquid). The gravitational redshift inside the sphere is produced by the non-Newtonian force of repulsion (which is due to the $\lambda $-term, $\lambda $~=~3/a$^{2}$~$>$~0); it is also calculated.