Derivation of the Equations for the Gravitational Field of a Condensing Cosmogonical Body within the Framework of Statistical Theory

Abstract This paper considers the statistical theory of cosmogonical bodies formation in order to derive equations for the gravitational field of a condensing cosmogonical body. Starting the conception for forming a spheroidal body inside a protoplanetary nebula, this theory solves the problem of gravitational condensation of such a cloud in a view to planetary formation in its own gravitational field. Within the framework of the statistical theory, new models and evolutionary equations of statistical mechanics have been obtained. It is shown that the presence of a dark matter (DM) (or an ethereal medium) around a gravitationally interacting mass serves as a basis for their gravitational interactions and gravitational wave propagation. First, the equation of motion of a “liquid” particle in a “quasi-solid” approximation inside a spheroidal body in gravitational and inertial fields is considered. Using the gravimagnetic vector potential introduced, the equation of motion for a solid particle with DM surrounding in gravitational and gravimagnetic fields is obtained. Taking into account this equation, the first system of equations of the gravitational/gravimagnetic field is derived. Using both the Lagrange function of a moving “liquid” gaseous–ethereal particle (with a “solid” core) in the gravitational/gravimagnetic field and the Lagrange function of the same field, the expression of a total action for the gravitational/gravimagnetic field and matter is obtained. Applying the least action principle and varying only the gravitational potentials together with the anti-diffusion velocity (but not the coordinates), the second system of equations of the gravitational/gravimagnetic field of a condensing spheroidal body is derived. Using these equations, the total energy of the gravitational/gravimagnetic field and gravitating matter as well as the density and gravitational energy flow are estimated. We show that the Newtonian approximation (following from Einstein’s GR) does not fully describe the gravitational field of gravitating masses, while in the framework of the proposed statistical theory the mentioned equation of particle motion in an arbitrary non-inertial frame of reference can be obtained.