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

It is shown that, according to the General Relativity, only the transverse metric distances – the transverse comoving distance and the angular diameter distance similar to it – can obey the Hubble linear dependence. The transverse comoving distance belongs to the comoving reference of spatial coordinates and time in the expanding Universe and is determined by the redshift of the emission wavelength.

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.

Anisotropy of the luminous intensity of distant astronomical objects of expanding Universe in intrinsic space of the observer is shown. The relativistic distance-luminosity relation, by which radial coordinate of astronomical object is being determined taking into account Hubble anisotropy of its luminous intensity, is received. As it follows from this relation, values of radial coordinates of distant astronomical objects in intrinsic space of the observer are much smaller than values of their coordinates, calculated by classical distance-luminosity relation. This makes the presence of such hypothetical components of the Universe as dark matter and dark energy unnecessary in principle

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.