Phenomenological justification of the Lorentz contraction the length and gauge justification of the special theory of relativity (SR) are set out. We prove the mutual consistency of the SR and the existence of ether. The physical essence of the twins paradox shows. FR Schwarzschild solution is based on assumptions about the evolutionary isoenergetic contraction of matter at the level of elementary particles. This contraction causes expansion Universe in Schwarzschild FR. The phenomenon of gravity is a consequence of physical inhomogeneity of space. It is caused by the tendency of matter to minimize its energy at rest. Investigated various non-rigid frame reference of spatial coordinates and time (FR). Unobservable Lorentz excess of reducing the radial dimensions and metrically nonuniform compression of microscopic matter (as a result of the gravitational polarization of the ether in the FR evolutionarily contracting matter) are the cause of the curvature of its own space of matter. The latter contains all the absolute unlimited space inside observer horizon.

The cardinal difference between relativistic gravithermodynamics (RGTD) and general relativity (GR) is that in RGTD the extranuclear thermodynamic characteristics of matter are used in the tensor of energy-momentum to describe only its quasi-equilibrium motion. For the description of the inertial motion in RGTD only the hypothetical intranuclear gravithermodynamic characteristics of matter are used. Exactly this fact allows avoid the necessity of non-baryonic dark matter in the Universe in principle. Evolutionary self-contraction of microobjects of lower layers of gravithermodynamically bonded matter outpaces the similar self-contraction of its upper layers. This is the exact reason of the curvature of intrinsic space of matter. That is why gravitational field itself should be primarily considered as the field of spatial inhomogeneity of evolutionary decreasing of the size of matter microobjects in the background Euclidean space of expanding Universe. In correspondence to this the gravitational field itself is the field of spatial inhomogeneity of gravithermodynamic state of dense matter of compact astronomical objects, as well as of strongly rarefied gas-dust matter of space vacuum. And, therefore, the gravitational field fundamentally cannot exist without matter. That is why it is not an independent form of matter. It is shown that equations of the gravitational field of 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. Only conditional identity of inertial mass of moving matter to its gravitational mass only by gravity-quantum clock, which is located in the point, from which the matter started its inertial motion, and due to the usage of corrected value of gravitational constant in its pseudo-centric intrinsic frame of reference of spatial coordinates and time, is justified. This is related to the equivalence of inertial mass of matter to the Hamiltonian of its inert free energy, while the gravitational mass of matter is equivalent to the Lagrangian of its ordinary rest energy. The identity of the multiplicative component of the Gibbs free energy to the ordinary rest energy of matter, which is equivalent to its gravitational mass, is substantiated. It was proved that values of thermodynamic internal energy and Gibbs free energy of matter of inertially moving body are equal in all global gravithermodynamic frames of references of spatial coordinates and time (GT-FR) that are also inertially moving relatively to matter. The temporal invariance of not only the momentum but also of Lagrangian of ordinary rest energy and of equivalent to it gravitational mass of matter is justified. And that is precisely why there is the temporal invariance and a conformal Lorentz-invariance of thermodynamic potentials and parameters in examined modification of transformations of the special theory of relativity (SR). Conformal relativistic transformations of increments of metrical spatial segments and metrical temporal intervals (instead of increments of coordinates and coordinate time of SR) were received. Exactly this fact allows avoid not only the twins paradox when twins are inertially moving but also the necessity of the dark energy in the Universe. It is also shown that the tensor of energy-momentum of matter (right side of the gravitational field equation) should be formed not being based on external thermodynamic parameters, but being based exactly on the intranuclear gravithermodynamic parameters. The canonical differential equation of the dynamic gravitational field (that corresponds to matter, which moves in this field only by inertia) is examined. It is this equation that determines the spatial distribution of the average density of mass of matter in the quasi-equilibrium state of its motion by inertia. 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. The standard value of the average density of matter gravitational mass at the edge of a galaxy is determined by the cosmological constant Λ and the difference between unity and the maximum value of the parameter bc. And it is a nonzero standard value, despite the local gravitational radius at the edge of a galaxy takes the zero value. It is shown that the decrease in the strength of the gravitational field of flat galaxies is inversely proportional to the radial distance, and not its square, and that the increase in the gravitational "constant" is inversely proportional to the fourth degree of the limit velocity of surface hydrogen individual (separate) motion. Consequently, the presence of dark non-baryonic matter in the Universe is unnecessary. Of course, bodies’ free fall in gravitational field is an original realization of their tendency to increase the evolutionary self-contraction of microobjects of their matter, and the realization of the tendency of the whole gravitationally bonded inhomogeneous matter to the minimum of the integral values of its inert free energy and thermodynamic Helmholtz free energy. Bodies that fall accelerate independently in spatially inhomogeneous medium of the outer space or atmosphere. Such bodies transform their continuously released intraatomic energy into kinetic energy. It is shown that in case of bodies’ free fall the gravitational deceleration of the rate of their intrinsic time is completely compensated by the motion due to isotropic all-round conformal gauge selfcontraction of the size of falling bodies in the background Euclidean space of the Universe. Clocks that fall free are inertially moving and, therefore, continue to count time at the same rate as when they were in the state of rest. Similarly, the rate of time of astronomical body is not changed in the process of its motion in elliptical orbit. The dilation of intrinsic time of distant galaxies is also absent, which points on the fact that Etherington identity does not correspond to reality. The fact that Hubble’s redshift is linearly dependent on transversal comoving distance instead of luminosity distance is justified. It is shown that mentioned above fact corresponds to astronomical observations. According to this the presence of dark energy in the Universe is also unnecessary. For the collective gravithermodynamic Gibbs microstates the connection between all thermodynamic potentials and parameters of matter have been found. This connection is realized with the help of several wave functions that can take arbitrary values with certain probability. The quantum equation of gravitational field have been found, the solutions of which set the spatial distribution of gravitational radius of matter in its every new gravithermodynamic state with the polynomial function with the next more high degree. The indicator of the degree of this function of continuously cooling down matter can successively take only integer and semi-integer values. That is why the process of cooling down of the whole RGTD-bonded matter is the quantum process that is caused by its spontaneous transition to the polynomial function with more high value of degree and, therefore, to the next quantized collective gravithermodynamic state.

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. Gravitational field is not an independent form of matter. Bodies free fall in gravitational field – is an original realization of tendency of the whole gravitationally bonded inhomogeneous matter to the minimums of the integral values of enthalpy and Gibbs free energy. Bodies that fall independently accelerate in spatially inhomogeneous medium of the outer space or atmosphere. Such bodies transform their continuously released intra-atomic energy into kinetic energy.

Only conditional identity of inertial mass of moving matter to its gravitational mass only by gravity-quantum clock, which is located in the point, from which the matter started its inertial motion, and due to the usage of corrected value of gravitational constant in its pseudo-centric intrinsic frame of reference of spatial coordinates and time (FR), is justified. This is related to the equivalence of inertial mass of matter to the Hamiltonian of its inert free energy, while the gravitational mass of matter is equivalent to the Lagrangian of its internal energy.

The quantum equation of gravitational field have been found, the solutions of which set the spatial distribution of gravitational radius of matter in its every new gravithermodynamic (GTD) state with the polynomial function with the next more high degree. The indicator of the degree of this function of continuously cooling down matter can successively take only integer and semiinteger values. That is why the process of cooling down of the whole GTD-bonded matter is the quantum process that is caused by its spontaneous transition to the polynomial function with more high value of degree and, therefore, to the next quantum state.

The equations that combine the instantaneous values of main thermodynamic parameters and potentials (that are characteristic to Gibbs thermodynamic microstates) of the simplest gases and liquids were found. The maximum possible (limit) velocity of matter transfer and the four wave functions and derivatives from them, which can take with certain probability any arbitrary instantaneous values, are used as thermodynamic hidden parameters and variables in these equations. Such gases and liquids can gradually (evolutionally) quasi-equilibrium cool down with self-creation of stable gravitational fields due to electromagnetic interactions of their molecules. In those fields the local values of characteristic intensive parameter are saved in time and corresponding to it characteristic extensive parameter is the same in the whole space at the same time. The electro-magnetic nature of gravitational field in matter was justified. It was proved that hypothetical ideal matter (ideal gas, ideal liquid) in principal cannot self-create gravitational field due to the absence of electromagnetic interaction of its molecules. The dependencies of physical and other thermodynamic characteristics of matter on the hidden parameters and variables were examined.

Generalized relativistic transformations of increments of coordinates and rime are examined. These transformations take into account possible influence of thermodynamic state of moving matter on its relativistic deformation and on the dilation of its proper time. It is shown that these transformations cause only inhomogeneous angular distribution of relativistic values of gravibaric velocity of light, which is an alternative to coordinate-like velocity of light in General Relativity. Also these transformations cause the presence of scaling factor in time-like interval. The possibility of experimental verification of the influence of pressure in moving matter on relativistic dilation of its proper time is examined.

Equations of thermal state of matter, which satisfy Tolman condition for thermal equilibrium in spatially inhomogeneous equilibrium states of matter and guarantee the possibility of adiabatic cooling-down of this matter in the early Universe uniformly filled by it, are examined. It is shown that all thermodynamic parameters and characteristics of such matter are determined or interconnected by the relations, which includes gravitational constant, as well as cosmological constant l (or Hubble constant that is determined by it). This denotes the thermodynamic nature of both gravitational field inside of matter and the phenomenon of Universe expansion. All results are obtained here being based on initial statements of General Relativity and, therefore, they do not fully correspond to gravithermodynamics, which conceptually differs from General Relativity, in fact.

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 author has analyzed historical roots of discussed here misconceptions and misunderstandings and has shown the possible ways to overcome them. Such constructive approach gives us the hope for getting rid of the majority of revealed here misconceptions and misunderstandings. Unfortunately, this is the problem of not only the astronomy and cosmology, but also of physics in general. Our perception and reflection of physical reality is still very primitive and, foremost, mainly mechanistic, macrocentric and anthropo-limited. The unreality of black holes, Big Bang, non-baryonic dark matter, dark energy, photons and neutrinos is justified in details. The current usage of exponential scale instead of metrically homogeneous scale of cosmological time in cosmology is shown. Therefore, the ignorance of the fact that only the infinitely far cosmological past on the event horizon and infinitely far cosmological future on Schwarzschild sphere are simultaneous with any event in people’s world is shown. The ignorance of the fact that this pseudo-horizon covers the past of all infinite Universe is also shown. The possibility of existence of antimatter inside the neutron stars and quasars that have the hollow body topology and mirror symmetry of their intrinsic space is justified. The big redshift and long lasting high luminosity of quasars are explained. The spatio-temporal noninvariance of the gravitational constant and the fictiveness of Etherington's identity are proved. The absence of gravitational fields in the Universe up to the moment of discontinuity of its uniform gas continuum is shown. The origination of the gravity phenomenon is related to the formation of spatially inhomogeneous thermodynamic states by the matter and to the tendency of the whole gravithermodynamically bonded matter to reach the minimum of the integral values of its inert free energy and Gibbs free energy. The temporal invariance of not only all thermodynamic parameters and potentials of matter and its momentum but also of Lagrangian of ordinary rest energy and of equivalent to it gravitational mass of matter (to which the inertial mass is identical only in intrinsic time of this matter) is justified. The fact that spatial distribution of gravitational field strength, defined by logarithmic gravitational potential, perfectly corresponds to astronomical observations is shown. It is shown that according to the General Relativity and the Relativistic Gravithermodynamics equations, the configuration of the dynamic gravitational field of a galaxy in a quasi-equilibrium state corresponds to reality. The fact that Hubble’s redshift is linearly dependent on comoving distance instead of luminosity distance is justified. It is shown that mentioned above fact corresponds to astronomical observations. It is concluded that such concepts as corpuscle and elementary particle are purely macroscopic. The inadmissibility of the presence of “thing-in-itself” in physics is shown. The possibility of spiral-wave nature of the matter microobjects – the terminal local drains of turns of the spiral waves of high frequency space-time modulations of the dielectric and magnetic permeabilities of the physical vacuum (singularities of the field according to Einstein hypothesis) – as a whole is shown.

The general solution of the equations of the gravitational field of the galaxy with an additional variable parameter is found. A typical dependence of the zonal velocity of the orbital motion of stars on the parameter b=(vc/c)² and on the radial distance r to the center of the galaxy has the following form: V=Ve{[(b/be)n+(be/b)n]/2}-1/2= c{[2nln(r/re)]2+(c/Ve)4}-1/4, where: vc – coordinate velocity of light, re – the radius of the friable galactic nucleus, on the surface of which the linear velocity of the orbital motion of stars can take its maximum value Ve, n – additional variable parameter that determines in GR the distribution of the average mass density mainly in the friable galactic nucleus. The velocity V is close to Kepler only for n>2²⁵. At n<2¹⁵, it is slightly less than Ve, even at the edge of the galaxy. The maximum allowable value of the average mass density of a substance outside the friable galactic nucleus [μ]≈V2/4πGr2 negligibly weakly depends on the parameter n in GR. If the energy-momentum tensor is formed not on the basis of external thermodynamic parameters, but on the basis of intranuclear gravithermodynamic parameters of the substance, then the dependence of the average mass of the substance on the value of the parameter n becomes very significant. The permissible value of the average mass density of matter outside the friable galactic nucleus [μ]=b[2V2c-2-(a-1)]/(1-b)aκc2r2 is determined by the value of the parameter a, which is responsible for the curvature of space. And it can be arbitrarily small. Therefore, in relativistic gravithermodynamics, in contrast to GR, there can be no shortage of baryonic mass.

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 General Relativity the distribution of the average mass density mainly in the friable galactic nucleus. The velocity of the orbital motion of stars is close to Keplerian one only for n > 2²⁵. At n < 2¹⁵, it is slightly less than the highest possible velocity even at the edge of the galaxy. 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. After all, this spatial distribution of the average mass density of the galaxy's matter is itself determined by the standard configuration of its dynamic gravitational field. The standard value of the average mass density of matter at the edge of a galaxy is determined by the cosmological constant Λ and the difference between unity and the maximum value of the parameter b_c. And it is a non-zero standard value, despite the gravitational ra-dius at the edge of a galaxy takes the zero value. Therefore, in Relativistic Gravithermodynamics, in contrast to General Relativity, there can be no shortage of baryonic mass.

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, and not by the weak gravitational pseudo-forces at the edge of the galaxy. The strength of the dynamic gravitational field of spiral and other flat (or superthin) galaxies, according to their two-dimensional topology, is inversely proportional to the radial distance, not to its square. And this is the case, despite the inverse proportionality of the strength of individual gravitational fields of all spherically symmetric astronomical objects of the galaxy exactly to the square of radial distance. The general solution of the equations of the gravitational field of the galaxy with an additional certain parameter n is found. At possible values of n < 1, the velocity of the orbital motion of stars is slightly less than the highest possible velocity even at the edge of the galaxy. According to the General Relativity (GR) equations and 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. After all, this spatial distribution of the average mass density of the galaxy's matter is itself determined by the standard configuration of its dynamic gravitational field. The standard value of the average mass density of matter at the edge of a galaxy is determined by the cosmological constant Λ and the difference between unity and the maximum value of the parameter b_c. And it is a non-zero standard value, despite the gravitational radius at the edge of a galaxy takes the zero value. Therefore, in the RGTD, in contrast to the GR, there can be no shortage of baryonic mass.

It is shown that, according to 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 transverse comoving distance DM=(c/H)z belongs to the comoving frame of reference in the expanding Universe (CFREU) and is determined by the redshift of the emission wavelength z=Δλ/λ0. The angular diameter distance DA=-(c/H)ž belongs to the frame of reference (FR) of the observer of an expanding Universe and is determined by the redshift of the frequency of the emission wave ž=Δν/ν0= -z/(1+z). The luminosity distance DL=(c/H)(1+z)1/2z is not the transverse metric distance and therefore its dependence on redshift is nonlinear. It is taken into account that the Hubble constant, like the length standards and the constant of the velocity of light c, is a fundamentally unchangeable quantity in the rigid FRs. Its exact value is empirically found H=с(Λ/3)1/2= (π4α/8NDn)νbn= (2π/3)αtp2(πνbn/2)3= (2π/3)Ge2(mn/4ħ)3= 2,018859•10-18 [s-1]= 62,29548 [km/sMpc], where: Λ is the cosmological constant, NDn=1,5(tpνbn)2= 3πchmn-2/G= 0,999885•1040 is the neutron large Dirac number, α=e2/cħ is the fine structure constant, νbn=mnc2/2πħ is the de Broglie wave frequency of the neutron, tp=(c5ħG)1/2 is the Planck time, ħ=h/2π is the Dirac-Planck constant, G is the Newton’s gravitational constant, e is the electric charge of the proton and electron, mn is the mass of neutron. 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 FR of observer. Etherington did not take into account the fact that the Universe is homogeneous only in CFREU, and recklessly made a “cocktail” of the phenomena and features inherent in two different FRs.

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 pseudoforces 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. The strength of the dynamic gravitational field of spiral and other flat (or superthin) galaxies, according to their two-dimensional topology, is inversely proportional to the radial distance, not to its square. And this is the case, despite the inverse proportionality of the strength of individual gravitational fields of all spherically symmetric astronomical objects of the galaxy exactly to the square of radial distance. The general solution of the equations of the gravitational field of the galaxy with an additional certain parameter n is found. At possible values of n < 1, the velocity of the orbital motion of stars is slightly less than the highest possible velocity even at the edge of the galaxy. According to the General Relativity (GR) equations and the Relativistic Gravithermodynamics (RGTD) equations, the configuration of the dynamic gravitational field of a flat 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. After all, this spatial distribution of the average mass density of the galaxy's matter is itself determined by the standard configuration of its dynamic gravitational field. The standard value of the average density of mass of matter at the edge of a galaxy is determined by the cosmological constant Λ and by the difference between unity and the maximum value of the parameter bc. And it is a non-zero standard value, despite the gravitational radius at the edge of a galaxy takes the zero value. Therefore, in the RGTD and in the appropriate interpretation of the GR, in contrast to the orthodox interpretation of the GR, there can be no shortage of baryonic mass. And therefore, the Universe does not need dark non-baryonic matter at all.

For the collective gravithermodynamic Gibbs microstates the connection between all thermodynamic potentials and parameters of matter have been found. This connection is realized with the help of four hidden wave functions that can take arbitrary values with certain probability. The possibility of obtaining the known equations of thermodynamic state of real gases is shown based on the use of both the coordinate velocity of light of the general relativity and the mathematical expectations precisely of these four hidden parameters (wave functions) and functions of them. It is substantiated that in a quasi-equilibrium state, a real gas has spatial homogeneity not only of its entropy but also of the resulting extensive parameter (an indicator the compressibility coefficient). But the radial values of resulting intensive parameter (an indicator of hierarchical complexity and of quasi-equilibrium of cooling down) of a real gas are invariant in time. It has been proven that the orthodox interpretation of general relativity is not consistent with gradually cooling matter and therefore with the evolutionary cooling of the early Universe.