The feasibility of using the equations of the dynamic gravitational field to reflect the expanding Universe has been proven. The fallacy of using such a false parameter as the coordinate velocity of light in GR is proven. This coordinate velocity of light, unlike the limit velocity of matter, cannot in principle be less than the true velocity of matter.

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.

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.

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.

Показано, що спеціальна та загальна теорії відносності відображають калібрувальність дії на речовину відповідно руху та гравітації. Це не дозволяє спостерігати у власному просторі та часі речовини будь-яких змін, що виникли через цю дію. Знайдено розв’язок рівнянь гравітаційного поля, що відповідає астрономічним тілам, які альтернативні чорним дірам. Показана вічність існування Всесвіту як у майбутньому, так і у минулому

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.

The initial cause of unambiguously younger age of the second twin than age of the first twin at the moment of their meeting is pointed. This initial cause is not the accelerated motion of the second twin, but the fact of changing of its direction or just the velocity of its motion in space itself and, consequently, the fact of its transition from one inertial reference system of spatial coordinates and time (IFR) to another. This is concerned to changing in new IFR of spatial as well as of time coordinates of events, which have realized before, including events, information about which have not come to the twin by the moment of its transition to new IFR. It is shown that imaginary twin paradox (clock paralogism) takes place in general relativity (GR) only because of the impossibility of mutual distinguishing of standard time (path-like proper time of moving object) and coordinate-like internal time of the IFR (or any other FR) and because of neglect of the necessity of re-calculation of events time coordinates as a result.

It is shown here that Lorentz transformations are caused by gauge effect of motion on matter (principle nonobservability of effect of motion on matter). This gauge effect of motion is caused by interdependence and mutual determination of propagation velocity of interaction between matter elementary particles and of rate of course of matter proper (standard) time. The Lorentz transformations are derived without any linearity assumptions and being based only on the presence of relativistic shrinkage of the length of moving body and on clock desynchronization at its slowest transfer along this body.

The possibility of getting a linear element (interval) of Schwarzschild frame of reference of spatial coordinates and time (FR) is shown, founded on the existence of fundamental (Newton absolute) space, which is formally independent on matter and is only a container for it [1]. In addition to it, the presence of evolutionary changeability and spatial inhomogeneity of properties of the physical vacuum (PV), filling all this absolutely rigid (nonexpanding) Euclidean (noncurved) infinite space, is assumed.

Показано, что преобразования Лоренца соответствуют калибровочности (принципиальной ненаблюдаемости) воздействия на вещество его равномерного движения и, на самом деле, являются преобразованиями приращений лишь координат, а не метрических отрезков. Эта калибровочность воздействия движения обусловлена взаимозависимостью и взаимной определимостью скорости распространения взаимодействия между элементарными частицами вещества и темпом течения собственного времени вещества. Необходимость перехода от приращений координат к приращениям метрических отрезков обусловлена ковариантностью физических законов относительно преобразований координат и времени лишь в собственных пространствах, в которых принципиально не наблюдается, как гравитационная, так и релятивистская деформация вещества на уровне его элементарных частиц. Поэтому вместо релятивистского сокращения длины движущегося тела имеют место сопутствующие ему кинематическая кривизна а, следовательно, и анизотропия заполненного движущимся веществом участка собственного пространства наблюдателя этого движения.

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) is substantiated. This can take place in the case of counting of cosmological time in frame of reference of coordinates and time (FR) not co-moving with matter, in which by the Weyl hypothesis galaxies of the expanding Universe are motionless. The absence of any limitations of the value of mass of astronomical body, which self-contracts in Weyl FR, when it has hollow topological form in the space of Weyl FR and mirror symmetry of its intrinsic space, is shown. Because of this symmetry, both external and internal boundary surfaces of body are observed as convex. At that, in the "turned inside out" internal part of the intrinsic space (in the Fuller-Wheeler lost antiworld) unlike external part, instead of the phenomenon of expansion phenomenon of contraction of "internal universe" is observed.