Phenomenological theory of gravitational vacuum

An idea is developed that the vacuum in the gravitational field acquires properties of an elastic medium described by a definite tension _ik. The vacuum is stated to also participate in the formation of the space-time metric, together with the usual matter. So, the matter, vacuum and metric form a complex unity determined by the solution of the field equations. The vacuum may prove to play an essential role in the extremely strong fields existing in superdense celestial bodies. The tensor _ik is not to be identified with the pseudo-tensor of the energy-momentum of the gravitational field the idea of which is preserved.The problem of vacuum is investigated in the case of the central symmetry static field. A number of properties of the tensor _ik is found using the symmetry of the field and comparison with the post-Newton limit. The external and internal problems, as well as the procedure of joining the solutions on the surface of a celestial body, have been formulated. The stellar surface is determined in the usual way:P(r) = 0 whereP is the matter pressure. The theory includes three dimensionless parametersa=p/,b=p/ (,p, p are the density of the vacuum energy and of its pressures in the radial and transverse directions) and determining the vacuum elastic properties. Generally speaking, they depend on the valueP/c² in the stellar centre where is the mass density. From general physical considerations it is shown that 0 1 + lim_P (l/q). The field equations are solved for the simple version of the theoryb=–a. There are solutions corresponding to superdense celestial bodies with masses considerably exceeding that of the Sun.