The correspondence of the parameter b of the Schwarzschild solution of the gravitational field equations to the square of the relative frequency of electromagnetic interaction of micro-objects of a stationary matter and its equivalence to the square of the maximum possible (limit) velocity of this matter on a singular surface are substantiated.

The possibility to avoid physical realizability of cosmological singularity (singularity of Big Bang of the Universe) directly in the orthodoxal general theory of relativity (GR) and in its improved version – the relativistic gravithermodynamics (RGTD) is substantiated.

Доведена доцільність використання для відображення розширного Всесвіту саме рівнянь динамічного гравітаційного поля. Лише завдяки цьому Габблова швидкість руху речовини не буде перевищувати швидкість світла на обрії подій Всесвіту.

The feasibility of using the equations of the dynamic gravitational field to reflect the expanding Universe has been proven. Only thanks to this, the Hubble velocity of matter will not exceed the velocity of light at the event horizon of the Universe.

The solution to the gravitational field equations of a flat galaxy has been found. It is shown that at the edge of the galaxy the excessively strong ordinary (unreduced) centrifugal pseudo-forces of inertia are compensated mainly by centripetal pseudo-forces of evolutionary self-contraction of matter in the background Euclidean space of expanding Universe, and not by the weak gravitational pseudo-forces at the edge of the galaxy.

In a galaxy that is not a continuous astronomical self-formation the coordinate velocity of light can be significantly greater than zero on the median surface with the minimum possible value of the Schwarzschild radius. After all, the prevention of the annihilation of stars containing antimatter with stars containing matter is ensured by their rotation around the median surface, which does not allow them to fall onto this surface, and even more so to cross it.

According to the Relativistic Gravithermodynamics (RGTD) equations, the configuration of the dynamic gravitational field of a galaxy in a quasi-equilibrium state is standard (canonical in RGTD). That is because it is not determined at all by the spatial distribution of the average mass density of its non-continuous matter.

Thermodynamical interpretation of General Relativity, consideration of the Universe as a single spiral-wave formation, and consideration of the so-called elementary particles and quarks as finite local flows of these spiral waves actually allowed the creation of a "theory of everything".

It was shown that Etherington’s identity is paralogism. Etherington’s identity is based on the imaginary relativistic dilation of intrinsic time of the galaxy by (1+z) times, but the presence of a relativistic anisotropy of luminosity of stars quickly moving away from it is ignored in the frame of reference of spatial coordinates and time of the observer.

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.

It is shown that, according to General Relativity (GR), only the transverse metric distances – the transverse comoving distance and the angular diameter distance similar to it – can obey the Hubble linear dependence.

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.

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.