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.

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.

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.

It is shown that equations of the gravitational field of General Relativity should be considered just as equations of spatially inhomogeneous thermodynamic state of 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. Gravitational field itself is the field of spatial inhomogeneity of thermodynamic state of dense matter of compact astronomical objects, as well as of strongly rarefied gas-dust matter of space vacuum.

В соответствии с физическими представлениями Эйнштейна о свободном (инерциальном) движении тел по геодезическим мировым линиям пространственно-временного континуума рассмотрена возможность инерциального (изоэнергетического) протекания эволюционного процесса расширения Вселенной и при не нулевом значении космологической постоянной уравнений гравитационного поля общей теории относительности. Это позволяет избежать потребности наличия во Вселенной «темной энергии». Показано, что классическим фотометрическим методом, не учитывающим, как соответствующую антигравитационному полю кривизну конечного собственного пространства наблюдателя, так и релятивистскую деформацию угловых апертур далеких галактик, определяются не фотометрические расстояния до этих галактик в этом пространстве.