The equivalence of only inert free energy of matter (and not of the total internal energy) to gravitational and inert masses is justified. It was proved that total energy of matter of inertially moving body is equal in all frames of references of spatial coordinates and time that are moving relatively to matter. And that is precisely why there is a conform Lorentz-invariance of thermodynamic potentials and parameters in examined modification of transformations of the special theory of relativity

The most perfect modification of the special and general theories of relativity is considered. It is shown that equations of the gravitational field of General Relativity (GR) should be considered as equations of spatially inhomogeneous gravithermodynamic state of only utterly cooled down matter. This matter can only be the hypothetical substances such as ideal gas, ideal liquid and the matter of absolutely solid body. The real matter will be inevitably cooling down for infinite time and never will reach the state that is described by the equations of gravitational field of the GR.

The general solution of the equations of the gravitational field of the galaxy with an additional variable parameter n is found. The additional variable parameter n determines in GR the distribution of the average mass density mainly in the friable galactic nucleus. The velocity of the orbital motion of stars is close to Kepler only for n>225.

The majority of theoretical misconceptions and the most significant misunderstandings in modern astronomy, cosmology and physics are caused by a purely mathematical approach and ignoring philosophical comprehension of physical reality and, as a result, by not deep enough understanding of the essence of certain physical phenomena and objects. Foremost, it's all about phenomena and objects that are under consideration by Special and General Relativity.

The paper covers a model of generation of fundamental forces induced by neutrino interference with other particles. Neutrinos fill up vacuum and inter-vacuum space obtaining a long-range action. Fundamental binding “proton-neutrinoselectron” has been defined and its transformation under various conditions into atom of hydrogen or neutron is studied. The paper also considers structuring of nucleus and electron atomic shell. Electron is positioned on stationary shell creating intraatomic and interatomic forces. Fundamental forces are generated due to neutrinos interference of neutron, nucleon and atom. Proposed the impact of neutrinos on origin of gravitation.

Interrelation between gravitation and acts of nature is deemed as a hard proof that the Earth gravitation is a predominant fact in this cohesion. Neutrino flow pressuring towards the Earth center on its way is forming difference abnormal zones within atmosphere, hydrosphere and lithosphere. As a result we are exposed to such natural disasters as earthquakes, volcanoes and climatic changes. Sufficient energy to such acts may be released only due to gravitation.

It is shown, that special and general relativities reflect the gauge of effect on matter of, correspondingly, motion and gravity. This doesn’t allow us to observe in intrinsic space and time of the matter any changes, appeared because of this effect. The solution of gravitational field equations that corresponds to astronomical objects, alternative to black holes, is found. The eternity of Universe existence both in the future and in the past is shown.

It is shown here, that relativistic shrinkage of the length of moving body is realizing strongly synchronously with the change of its velocity and is continuously self-sustaining without the effect of any forces. This shrinkage is caused by inertial isobaric self-contraction of body matter and by propagation of changes of the strengths of inertia forces field together with the front of body intrinsic time. A mechanism of kinetic energy filling (accumulation) of a body is considered and propagation of the phase waves of perturbation of gravitational field at supraluminal velocity is substantiated here.

Gravitational-optical gradient lens, comoving with radiation, is formed in observer's frame of reference of time and spatial coordinates (FR) due to evolutional decrease of average density of matter in the Universe as well as due to evolutional decrease of refraction index of interstellar medium. This diverging lens and Hubble gravitational lens together form virtual image of all infinitely far points of Euclidean background space of FR, comoving with expanding Universe, on its focal surface, which is the imaginary observer horizon.