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The full version of abridged text of article from Journal "Naukovyi Visnyk VNU", 2009 and from the collection "Proceedings of all Ukrainian seminar from theoretical and mathematical physics TMP'2009" - Lutsk: Volyn'University Press "Vezha", 2009, p. 75; Reports at all Ukrainian seminar from theoretical and mathematical physics, Lutsk, 27.02-1.03.2009 and at the IV Gamov international conference, Odessa, 17-23.08. 2009
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.
Clausius's Hypothesis about opportunity of the heat death of the Universe (1865) and also the misconceptions about non-invariance of thermodynamics equations to relativistic transformations led to false conclusion that methods of thermodynamics cannot be applied to the analysis of evolutional processes in megaworld. It is known now that the Universe cannot cool down at any as long as possible finite time period. Self-organization of spatially inhomogeneous thermodynamic states and gravitational fields that correspond to those states prevent matter from complete cooling down. The thing that prevents unlimited growth of entropy in the Universe is the self-organization of different structural formations, the complexity of which grows with every new hierarchy level of self-organization of natural objects that form them. Relativistic generalization of thermodynamics with the invariant absolute temperature is currently considered as the most acceptable generalization [1; 2].
Thermodynamics was already used in this or that manner for analysis of the processes of formation of megascopic Universe objects [3 – 7]. The main researches that should be highlighted: researches on gravitational plasma [7; 8], researches based on the kinetic theory of rarefied gas , and also the theory of spatio-temporal evolution of nonequilibrium thermodynamic systems . Recently, being based on the analysis of self-organization processes in nonequilibrium systems  and on the more wide usage of the methods of statistical physics, thermodynamics of self-gravitating systems achieved the quite significant success [12 – 14]. However thermodynamic and gravitational descriptions of the self-organization processes of Universe astronomical objects are still not naturally merged. Therefore, phenomenological justification of the united nature of thermodynamic and gravitational properties of the matter  is very important for the studying of megascopic astronomical objects and global processes in the Universe.
Thermodynamic states of matter, examined in General Relativity (GR), are self-inducted by matter spatially inhomogeneous states of this matter. This fact is caused by the presence of gravitational field in matter: Gravitational field is the cause of spatial inhomogeneity of rates of intra-atomic physical processes in matter and, therefore, it inducts not only the curvature, but also physical inhomogeneity of intrinsic space of matter [16; 17]. In rigid frames of reference of time and spatial coordinates (FR) this physical inhomogeneity of the space is in the mutual inequality of values of such hidden thermodynamic property of the matter as coordinate-like velocity of light in different points of this space .
The equations of GR gravitational field should be considered as just the equations of spatially inhomogeneous thermodynamic state of utterly cooled down matter. Such matter can be represented only by hypothetical substances such as ideal gas, ideal liquid and matter of absolutely rigid body. Real matter is doomed to cool down infinitely long without reaching the state that is described by the equations of GR gravitational field. This state of gradual quasi-homogeneous cooling down is described by considered here modified tensor equations of GR – equations of relativistic gravithermodynamics (RGTD).
Increasing of coordinate-like velocity of light during the distancing from compact matter of astronomical body can be the consequence of gradual change of thermodynamic parameters of the atmosphere and the outer space that surround this body. In this case spatial distributions of coordinate-like velocity of light, which are set by gravitational field, strictly correspond to concrete spatially inhomogeneous thermodynamic states of matter. Adding of the third independent parameter – coordinate-like velocity of light to any of two mutually independent thermodynamic parameters in GR guarantees only conventional consistency of this theory with objective reality. Indeed, the solutions of equations of gravitational field for any cluster of gravitationally-bounded matter are always examined in conventionally empty Universe. However, the Universe is not empty and, as united solution of equations of gravitational field and equations of thermodynamics for ideal liquid shows , values of coordinate-like velocity of light are not vacuum values, but pseudovacuum gravi-baric values. They are determined by the values of thermodynamic parameters of ideal liquid accurate to gauge coefficient. Only this coefficient can be considered as pseudovacuum value of coordinate-like velocity of light. In the case of presence of both mechanical and thermal equilibriums in ideal liquid this pseudovacuum value of coordinate-like velocity of light is the same within the whole liquid, which self-organized its spatially inhomogeneous equilibrium state and gravitational field that corresponds to this state . This fact allows us to consider this vacuum value as gauge parameter, that interconnects spatial and temporal metrics and cannot be observed in hypothetical gravi-quantum intrinsic FRs (GQ-FRs) of matter and in people’s world FR in principle.
Conventionally empty space that surrounds such compact matter of The Universe has really never been empty and never will be completely empty. Even the highest cosmic vacuum should be considered as very rarefied gas-dust incoherent matter, which obey the thermodynamic laws the same as ideal gas of non-interacting molecules. The limitation of the velocity of physical bodies is indeed exists in such matter. However, this limitation is not related to the velocity of light in the matter or in hypothetic absolute vacuum. In airspace, as well as in dense matter, the charged micro objects (protons) can propagate faster than the velocity of light. That is confirmed by the origination of the radiation, found by Cherenkov, in this case. On the other hand, hypothetical velocity of propagation of intranuclear interaction (pseudovacuum velocity of light of GR) decreases while approaching the gravity center unlike the real velocity of propagation of electromagnetic interaction in matter, which increases. This is in a good correspondence with the fact that thermodynamic and gravievolutional processes have opposite directions and is related to the fact that velocity of propagation of electromagnetic waves in matter is greater when the temperature of the matter is greater. Due to the same reason the physical processes flow faster not on the surface but in hotter bowels of the astronomical objects despite the gravitational slowing down is predicted by GR for those processes.
Maximal possible velocity of matter
The reason for limitation of velocity of physical bodies is indeed the nature of matter movement in the space. Physical vacuum is not carried away by physical body. Matter is only the non-mechanic excitement of physical vacuum (space-time modulations of its physical characteristics). Therefore, the perception of high-frequency discrete movement of the body in the space as the continuous motion is similar to cinematographic perception of discrete change of image frame. The limitation of body velocity can be related to the fact that it is impossible to reach infinitely high frequency of discrete change of Gibbs collective thermodynamic microstate (quantum «hologram») of the whole its RGTD-bonded matter and to the fact that it is impossible to reach the zero value of the length of spatial step shift (quantum micromovement) of the body. This frequency and this micromovement are de facto the de Brogile frequency νB and wave length λB of the moving body. That is why instead of denying the possibility of moving body to overcome the velocity of light we should state the principal impossibility to reach the extremely big velocity vl=(vvB)1/2=vBmin, that corresponds to the tending of νB to infinity, and tending of λB=vl/νB to zero, when phase velocity of de Brogile wave propagation vB reaches its minimal value, equal to maximal possible group velocity vmax of the whole matter of the body (vBmin= vmax≡vl).
Physical essence of gravitational field
There is a thermodynamic quasi-equilibrium between gravitationally self-contracted compact matter and surrounding it arbitrary rarefied matter of the outer space. Therefore, pseudovacuum value of the coordinate velocity of light in this rarefied liquid matter cannot differ from pseudovacuum value of the coordinate velocity of light in the space filled in by compact matter. And, consequently, this value should be the same in the whole Universe space, filled by gaseous and liquid matter. Thus, vacuum value of the coordinate velocity of light, which is a gauge parameter, should be considered as strictly equal to the constant of the velocity of light с in the whole space, filled in by any gaseous and liquid matter that is in quasi-equilibrium thermodynamic (thermal and mechanical) state. And then, due to isotropy of radial distribution of the pressure in such matter we can reach the following conclusion. The fact that the rates of hypothetical gravi-quantum time differ in the points of matter, where values of gravitational potential are different, is caused only by inequality of thermodynamic parameters of the gaseous or liquid matter, which fills the whole space, in those points. And, therefore, such matter is not only in the state of mechanical and thermal equilibrium, but also on the same stage of evolutional decreasing of the level of improper value of its intranuclear energy.
Anisotropy of radial distribution of the pressure in matter is the characteristic for solid matter. That is why solid matter and liquid matter, located above the world Ocean level, are on the certain stage of lagging of evolutional decreasing of the level of improper value of its intranuclear energy. The water of world Ocean is also on the certain stage of lagging of this process since it covers the rigid body. It means that gravitational field is the field of non-equal (spatially inhomogeneous) lagging of evolutional decreasing of improper value of matter intranuclear energy.
In correspondence with all this, gravitational red shift of emission radiation spectrum can take place only for astronomical objects with a solid photosphere, as well as for liquid and gaseous astronomical objects, which are in non-equilibrium thermodynamic states. And, of course, gravitational redshift of radiation spectrum is the consequence of lagging of evolutional decreasing of intranuclear energy of radiating matter. Frequencies of emission radiations are determined only by the differences between energy atomic levels, values of which are not changed in atoms at quasi-equilibrium thermodynamic processes. Radial changes of matter RGTD-parameters, when liquid or gaseous matter is in hypothetical equilibrium thermodynamic state, lead to the change of only the frequency of quantum interactions in atomic nuclei. And it is not accompanied by redshift of its spatially homogeneous emission radiation and by widening of spectral lines of that emission radiation.
Thermodynamic nature of the majority of gravitational effects
Analysis of solutions of the equations of GR gravitational field [15; 19] specifies the thermodynamic nature of majority of gravitational effects. All gravitational phenomena, except the phenomenon of curvature of intrinsic space of matter, are strictly thermodynamic in fact. For example, the fact that bodies, more dense than surrounding medium, tend to the gravity center, as well as the fact that bodies, less dense than surrounding medium, tend from the gravity center, is caused by the fact that the whole system (which consists from all bodies and the medium surrounding them) tends to the state of the minimum of the integral value of their thermodynamic enthalpy . In the case of presence of heat exchange integral value of purely thermodynamic Gibbs free energy also tends to minimum, while integral value of entropy tends to maximum. From the other hand, the pressure in ideal gas and in any other incoherent matter is not caused by intermolecular electromagnetic interaction and, consequently, this pressure itself has purely gravitational nature. And, therefore, physical phenomena and properties of matter, which are examined by thermodynamics and theories of gravity in a different phenomenological way, are based on the same fundamental nature of matter micro-objects (elementary pseudoparticles) [16; 21].
In classical physics potential energy of gravitational field was considered as something external for the matter, while in GR potential energy is contained in matter itself. Indeed, free fall of the body is an inertial motion. Released potential energy of intranuclear bonds and intranuclear interactions in the atoms cores of matter of falling body together with the energies of nucleons that form these atoms transform into kinetic energy of body motion. And the excessive level of evolutionary lost intranuclear energy of matter, in fact, decreases. As it follows from united solutions of equations of gravitational field and thermodynamics equations [19; 21], all characteristics that determine gravitational properties of matter and phenomenon of Universe expansion are also contained in matter itself and cannot be considered as something external for the matter.
Gravithermodynamic FR of people’s world
In classical thermodynamics all intensive thermodynamic parameters of matter are determined via measuring of extensive parameters (which depend on those intensive parameters) of matter itself or matter of measuring instruments that are in thermal equilibrium with this matter. For example, the main method of temperature measuring is in the measuring of volume occupied by thermometer liquid. Pressure is determined via measuring of elastic deformation (caused by this pressure) of any element of recording instrument. Deformation and volume are both extensive parameters. This makes closed system of the pairs of mutually complementary intensive and extensive matter parameters self-consistent and guarantees invariance of intensive thermodynamic parameters to time transformations. And, thus, there is not only temporal invariance, but also Lorentz-invariance of used in thermodynamics proper values of intensive and extensive characteristics of matter. And it is similar to the principal invariance of the value of velocity of light by the intrinsic clock in the point of its dislocation and to the principal invariance of Hubble constant. The majority of measurings of physical characteristics in FR of people’s world is purely relative. They are strictly bonded not only to intrinsic clock, but also to other intrinsic instruments of operator who performs measurement. And, therefore, the influence of the instrument on the measurement result takes place not only in quantum, but also in classic physics. In contrast to microworld, in the macroworld the measurement results are only strictly determined.
And, therefore, invariant values of thermodynamic parameters and characteristics of motionless matter, which are used in classical thermodynamics, are self-sufficient and don’t need to be a member of any FR. They can be members only of certain tracking system: system that tracks changes of thermodynamic parameters and characteristics of matter. And, from the other hand, global FR can be formed based on this tracking system. The presence of phenomena, for which frequency of their elementary acts depends only on absolute temperature, is necessary for this global thermodynamic FR (GT-FR) to be non-artificial in nature. Then, the scale of absolute temperature can be linearly calibrated based on this frequency. The clock, using which the rates of hypothetical gravi-quantum proper times can be compared and dependences of these rates on parameters of thermodynamic states of these matters can be analyzed, can be realized based on this phenomenon.
And such phenomenon exists: dependence (obtained by Wien) of electromagnetic wave frequency, which corresponds to the maximum of spectral density of equilibrium thermal radiation, only on absolute temperature and proportionality of this frequency to absolute temperature. Therefore, united thermodynamic time is used in people world in fact, instead of gravi-quantum time, rate of which is not similar for different matters and depends on their thermodynamic states. Quantum processes in etalon matters can only be used for the counting of this time due to the stability of their rate in this matter when temperature T and pressure p remain unchanged. Thermodynamically invariant atomic characteristics – differences between energy levels ΔEij in atoms and frequencies of emission radiation νij=ΔEij/h (here h is the Planck constant) corresponding to them also can be used for this time counting. Energy levels are defined by radiuses of allowed orbits of electron shells in the atom and, similar to intensive thermodynamic parameter, are the characteristic defined by extensive parameter (radius of allowed orbit) and, therefore, dependent on transformations of spatial coordinates not time. Therefore, electrons energy and, thus, energy levels in atoms are, similarly to thermodynamic internal energy of matter U, Lorentz-invariant and does not depend on the level of inert intranuclear energy of nucleons as well as on the rate of hypothetic gravi-quantum intrinsic time of matter. And, therefore, the frequency of the same emission radiation remains the same within the whole matter that is located in spatially inhomogeneous equilibrium state in GT-FR, as well as in any other GQ-FR. It means that widening of spectral lines of emission radiation can be only Dopplerian – can be caused only by the thermal fluctuations of molecules of the matter. This is confirmed by the absence of gravitational smearing of spectral lines of excited atoms of cold rarefied galaxy medium even when values of their main quantum numbers are n≈1000 (λ=20 m) .
Absolute temperature is an intensive parameter that characterizes only the level of thermal internal energy U(T, p) of matter, which includes also potential energy of interatomic and intermolecular bonds. Invariance of all thermodynamic parameters and matter characteristics to time transformation denotes that all of them should be relativistic invariants. Therefore, temperatures of phase transitions should remain internal properties of moving matter. This means that the change of thermodynamic parameters and characteristics of matter should have indirect influence on the change of matter thermodynamic (inert) mass. And, therefore, nonchemical internal potential energy of interatomic and intermolecular bonds can transform into kinetic energy only of chaotic, but not directed, motion of matter molecules.
Inert intranuclear energy of matter
Not the total energy of matter UGT=E+U, but only the inert intranuclear energy E=mc2 can be equivalent to the inert mass m. Thermal internal energy of matter U can be considered analogically to kinetic energy and to electromagnetic radiation energy only as the external energy of molecules and atoms.
In classical thermodynamics the intranuclear energy considered as one that is not changed in thermodynamic processes. In fact, it is not true. Part of potential intranuclear energy of gas, which pressure is adiabatically increasing, transforms into energy of chaotic state of its nucleons and potential energy of stressed state of matter of the vessel that contains this gas . The release of intranuclear potential energy, which is reserved in deformed shell of the vessel that is in stressed state, takes place during the heating of compressed gas. Solid body freely expands during the process of its heating and the frequency of interaction of its nucleons decreases [15; 16]. Thus, dilation of its gravi-quantum time takes place in a similar way as it happens during body free fall. However, increasing of thermal energy of the body, which is accompanied by the increasing of his thermal temperature Т, is only non-significantly compensated by the decreasing of its intranuclear energy due to decreasing of intranuclear entropy SN, which corresponds to one mole of matter, and due to decreasing of intranuclear temperature TN. That is why no essential dependence of molar mass of matter on its thermal internal energy can be observed. And it takes place despite the presence of mutual correlation between inert energy E and purely thermodynamic Gibbs free energy G of matter. During the cooling down of the body non-significant part of its thermodynamic internal energy is spent on replenishment of inert intranuclear energy. The similar decreasing of frequency of interaction of nucleons and releasing of intranuclear energy that corresponds to it takes place during the experiments with rotating gyroscope.
Generalization of RTGD equation
Inert energy of matter should be taken into account in generalized differential equations of thermodynamics by means of multiplicative parameter of direct action fN=ηmvlb/c=(1-mcr-2c-4TNcr2SN2)1/2≤ (1+NRE2)1/2<2-1/2, which is proportional to the extremal value of local group velocity of matter vlb in an comoving FR in expanding Universe (CFREU) and, therefore, proportional to almost identical to it pseudovacuum coordinate-like velocity of light of GR in CFREU (vcbv=vlb) [15; 16]. These equations should also contain a multiplicative parameter of reverse action that realizes the negative feedback. Such parameter is obviously the relativistic external scale factor NRE=NE/ΓE=vl/vlb=(1-pNcr-2pN2)-1/2≥1, that increases while approaching the gravity center (and, therefore, while deepening into cosmological future) and is responsible for the curvature of intrinsic space of matter and for the presence of spatial inhomogeneity of intranuclear values of pressure pN and pseudo-volume VN. Here: ηm – parameter that corresponds to certain matter and that defines the dependence between fN and vlb; NE=r/R – external scale factor; r and R – radial coordinates of matter in GT-FR and CFREU correspondingly, ΓE – relativistic shrinkage of the length of radial segments of the body that happens due to its evolutionary self-contraction in CFREU, while TNcr and pNcr – not similar for different matters critical values of intranuclear temperature and pressure. In correspondence with this, the rate of quantum processes of intranuclear interaction between nucleons in global GT-FR can be characterized by relative average statistic value of frequency of this interaction fG=fNNRE=ηmvl/c<ηm, that is proportional to the extremal value of local group velocity of matter vl, in GT-FR (and, therefore, proportional to almost identical to it pseudovacuum coordinate-like velocity of light of GR in GT-FR vcv= vcbvNRE=vl [15; 16]). Precisely fG, similarly to vcv in GR, is responsible for the presence of gravitational pseudo-force FG, that forces matter for free fall. And this pseudo-force is proportional not to the mass, but to the Hamiltonian of the body H=const(r).
According to it, frequency of nucleons intranuclear interaction in GT-FR:
is equal to the division of the mass m of one mole of matter by the value of this mass mcr, which corresponds to «critical» equilibrium value GGTcr=GTcr+SNcrTNcr-VNcrpNc+mcrc2 of Gibbs free RGTD-energy:
It is obvious that not only mcr, ηm, TNcr and pNcr, but also GGTcr, GTcr, GNcr are individual parameters that characterize certain matter and are, possibly, related only to its certain aggregate or phase state.
Gibbs free RGTD-energy GGT, the same as Hamiltonian, is saved in the process of matter free fall. Moreover, GGT, the same as gravitational intranuclear Gibbs free energy GN, tends not to its minimum (in contrast to thermodynamic Gibbs free energy GT), but to its maximum during the process of body free fall and during the process of matter evolution. It is obvious that the tending of thermodynamic Gibbs free energy to its minimum is the partial compensation for gradual increasing of intranuclear Gibbs free energy. And since in CFREU: NEb=NEexp[HE(τ–τ0)]=NE/(1+z), ΓE=const(τ), fNb=fNexp[HE(τ–τ0)]=fN(1+z), then: fG=fNbNEb=fNNE=const(τ) and, consequently, in people’s world FR the evolutional increasing of Gibbs free RGTD-energy cannot be observed in principle. Here: HE – Hubble constant, that sets the speed of evolutional expansion of the Universe, τ – cosmological time, counted in CFREU by metrically homogeneous scale (dτ=dt), z – Dopplerian redshift of the wave length of radiation of astronomical object, characteristics of which are being determined. However in CFREU according to Hubble law both molar intranuclear Gibbs free energy and inert intranuclear molar energy are changed and, therefore, the also equivalent to it molar mass is changed:
Not only the molar mass itself ([1+z] times), but also its concentration in intrinsic space of the matter ([1+z]3 times) was bigger in that distant time . And it means that the need in “dark non-barionic matter” can be fictive.
While in all fast-flowing physical processes that are not accompanied by the performing of the work directed at the increasing of matter energy UGT, the Gibbs free RGTD-energy GGT can only increase (as it is expected) in case of isobaric (dp=0, dpN=0) heating of the body, the increasing of both intranuclear temperature dTN≥(S/SN)dT and intranuclear Gibbs free energy dGN=SNdTN-≥SdT takes place. And due to EGN=mcr2c4=const the following situation will take place. The inert intranuclear energy and corresponding to it gravitational mass of the matter will decrease the same number of times as intranuclear Gibbs free energy is increased. This is in a good correspondence with the results of experiments since for the many heated metallic bodies the decreasing of their mass is observed . In the process of cooling down of the body its intanuclear molar volume is increasing to its former value and intranuclear pressure will perform work to restore the former level of its inert energy (dE=pNdVN>0).
Spatially inhomogeneous equilibrium RGTD-state of liquid and gaseous matter takes place in the case of fulfillment of the following: GGTj=(fGi/fGj)GGTi. In the case of isotropy of radial distribution of physical parameters and characteristics of homogeneous matter of astronomical object it can be shown in the following way: fG(r)GGT(r)=const(r). In the case of radial altitudinal multi-layer distribution of inhomogeneous matter this condition is fulfilled layer by layer, with the break on the boundaries of two media: fG(k+1)GGT(k+1)<fGkGGTk, where (k+1) – serial number of the less dense and, therefore, more distanced from the Galaxy center matter.
In equations of GR gravitational field the thermodynamic enthalpy HT=GT+ST is de facto used instead of Gibbs free RGTD-energy. Equilibrium state of ideal liquid in GR is reached only in case of mutual absence of radial gradients of the following characteristics: Hg=HTvcv/c=const(r), Tg=Tvcv/c=const(r), S=const(r) . This conditions, supplemented by the condition of homogeneity of ideal liquid ηm=fGc/vcv=const(r), fulfill the more general RGTD condition of equilibrium state of liquids and gases:
Equilibrium RGTD-states of matter, in which external gravitational pressure of upper layers of matter is counterbalanced not only by intrinsic pressure inside matter, but also by radiation (thermal) pressure (Tg≠const(r)), are not considered at all in GR, in contrast to RGTD. And, therefore, GR not only reflect physical reality in more simple way, but also is applied to equilibrium states of only extremely cooled down homogeneous matter (Tg=const(r), ηm=fGc/vcv=const(r)). That is why the reflection of physical reality in GR should be considered only as the special case of its reflection in RGTD.
Internal energy U of real gases and liquids depends on many pairs of their intensive (Ai) and extensive (ai) thermodynamic parameters. However, it can also be shown as a sum of internal energy of hypothetic ideal gas (liquid) Uid and output of multiplication of resulting intensive (Aρ=TS/RT=T2S/pV) and extensive (aρ≡RT=pV/T) thermodynamic parameters:
where: Tid=TRT/RT0, Sid=SRT0/RT, Aρaρ=TidSid=TS. For gases: ai=RT0BiVi+1, Bi – virial coefficients that depend on both temperature and individual gas properties , while RT and RT0 – individual and universal gas constants correspondingly.
“Ideal” component Uid of internal energy is de facto identical to Helmholtz free energy FT, while “ideal” component HTid of enthalpy is identical to the Gibbs free energy GT.
This, of course, is caused by the absence of binding energy in ideal gas and ideal liquid due to the absence of electromagnetic interaction of their molecules and atoms. Self-organization of hierarchically more complicated interactions and interconnections in matter is in the tendency of Helmholtz and Gibbs free energies to their minimum.
Lower layers of matter, loaded by its upper layers form the extended system. The energy of such extended system  that consists of the whole RGTD-bonded matter is indeed equivalent to enthalpy. Moreover, as it is shown further, Aρ parameter takes the same value in the whole space filled by quasi-equilibrium cooling down homogeneous matter (∂Aρ/∂r=0). And, therefore, Gibbs energy “behaves” as it is expected and only changes in time. And when Gibbs energy changes in space it “behaves” like enthalpy (like the energy of extended system).
This is quite logical and reflected in static equations of GR gravitational field. However in dynamics the four-momentum should be formed not by enthalpy, but by Gibbs energy (free energy of extended system). And, of course, it should be not the Lorentz-invariant thermodynamic Gibbs energy, but relativistic intranuclear Gibbs energy.
So, if equations of GR gravitational field are designed to get the solutions that correspond only to ideal (extremely cooled down) matter, then the usage of enthalpy instead of Gibbs free energy in those equations is justified. But, of course, not the Lorentz-invariant thermodynamic enthalpy (intrinsic value of enthalpy), but Lorenz-noninvariant intranuclear enthalpy (improper value of enthalpy) should be used in those equations. However, in order to get the solutions that correspond to quasi-equilibrium cooling down astronomical objects we should include not enthalpy, which includes free and binding energy of extended system, but intranuclear Gibbs free energy with transition to functionally related to it thermodynamic Gibbs free energy (to the intrinsic value of Gibbs energy in FR of people’s world).
Spontaneous change of RGTD-state of coherent matter and, consequently, its free fall are possible only when they are accompanied by continuous decreasing fG and thereby decreasing of matter thermodynamic mass at rest.
Physical space that is rigidly connected with cooling down body self-contracts not only in CFREU, but also in intrinsic metric space of the body that has non-rigid intrinsic FR :
where: ρ – radial coordinate, which is counted by rigidly connected with body coordinate grid not in metric space but in physical space of gradually cooling down body, HT – parameter that characterizes the speed of observed shrinkage of the dimensions of cooling down body.
During matter free fall (dS=0, dV=0, dURGT=0) gravi-evolutional increasing of intranuclear entropy that is accompanied (as a compensation to its increasing) by increasing of molar value of intanuclear volume and, thus, by the release of intranuclear energy (instead of thermal energy) with its further transformation into kinetic energy of it ordered motion takes.
Obviously, in the tensor of the energy-momentum of GR gravitational fields equations we should use Lorentz-noninvariant intranuclear RGTD-characteristics of matter instead of Lorentz-invariant and temporally invariant thermodynamic characteristics. For gradually quasi-equilibrium cooling-down matter we should use the density of intranuclear Gibbs free energy GN/N=mcrc2/Vvcb=mcrc2ηm/VfGb instead of the density of enthalpy.
It should also be mentioned here that, according to GR and RGTD, the ideal gas (pV=RT0T) cannot have gravitational field in principle. Molar energy of ideal gas and, consequently, coordinate-like velocity of light in it are the same at all points of the space filled by this gas. And it means that the phenomenon of gravitation is related to electromagnetic interaction of molecules of matter and, therefore, has purely electromagnetic nature.
Generalized equations of thermodynamics
Thermodynamic processes in matter confront the intranuclear evolutionary and gravitational processes in it. When intranuclear Gibbs free RGTD-energy of matter is continuously increasing in CFREU, the thermodynamic Gibbs free energy in naturally flowing physical processes is tending to its minimum. Therefore, frequency of intranuclear interaction fG=fNNRE=ηmvl/c≤ηm corresponds to inversely proportional to it frequency of intermolecular electromagnetic interaction fI=χm/fG=qMNI=(vcm/c)NI=cχm/ηmvl≥/χm/ηm,, which is changing together with the change of velocity of light vcm in matter and with the change of internal scale factor NI=δlcr/δl≥1 of matter . Here: χm=χm0/Γm; Γm – relativistic shrinkage of the length of molecules of cooling down matter; χm0, ηm and δlcr – the constant or critical values of the parameters of a certain matter, which are not equal for different matters and not dependent both on strength of hypothetic gravitational field and on matter thermodynamic parameters.
In contrast to used in cosmology spatially inhomogeneous external scaling factor NE, which is the cause of the curvature of matter intrinsic space, internal scaling factor NI depends on thermodynamic state of matter and takes nonsimilar values for different matters. This factor characterizes the distinction between average statistic value of interaction distance δl in the atoms of concrete matter and the value of this distance δlcr that corresponds to critical equilibrium value of internal energy Ucr, Gibbs free energy GTcr, temperature Tcr, pressure pcr and radiation refractive index nm on the wavelength of maximum of energy of thermal radiation. And if qM=vcm/c=1/nm<1 characterizes the difference of real velocity of electromagnetic interaction propagation in matter from the constant of velocity of light с, then NI is responsible for compensation of the influence of decreasing of propagation velocity of electromagnetic wave on the frequency of electromagnetic interaction fI of matter microobjects. If for gases and simplest liquids the dependencies of instantaneous values of their thermodynamic parameters and potentials on qM and NI allow to separate these variables, then instantaneous value of their Gibbs free energy (that corresponds to their instantaneous thermodynamic microstates) can be expressed via these two parameters and via their function RT in the examined in current article way. Methods of thermodynamics allow us to analyze equilibrium states of matter even when there is no analytic dependence of thermal energy of matter on its thermodynamic parameters. With the purpose of revealing of some features let us examine analytic representation of such dependency for gases and simple liquids.
The comparison of reflection of physical reality in RGTD and in GR
For liquid and gaseous astronomical bodies, not containing solid nucleus, frequencies of interaction fG and fI are strictly determined by the values of pressure and temperature in matter. For solid or containing solid nucleus astronomical bodies those frequencies can also depend on the magnitude of lagging of evolutionary decreasing of their intranuclear energy. However, in equilibrium RFTD-states of the whole set of different matters the gradients of logarithms of fI and fG of all matters are strictly determined by gradients of pressure and temperature in them and, therefore, are strictly equal to the gradient of extremal velocity of motion vl of the whole RGTD-bonded inhomogeneous matter. Moreover, at the fulfillment of GNvl=const(r) condition the GNfG=GNvlηm/c=const(r), GT/fI=GTfG/χm=GTvlηm/χmc=const(r), GTvl=const(r) and GT/GN=const(r) conditions are also fulfilled within the borders of the whole RGTD-bonded continuous homogeneous matter that is in the state of mechanical and thermal equilibrium. All this allows using in the modernized GR only intranuclear properties of matter for the formation of metric tensor, but both intranuclear and thermodynamic properties of matter for the formation of energy-momentum tensor. However, Lorentz-invariance of pressure in the matter is ignored in the such modernized GR.
All the more so, separate contributions to gravitational potential of velocity of light in matter vcm and internal scaling factor NI are not important for the determination of gravitational pseudo-forces. However, the form of radial distribution of gravitational potential in space-time continuum (STC) of astronomical body that consists of this matter and the form of generalized relativistic linear element depend on their contributions . Therefore, the conversion of these characteristics are not gauge when the named contributions are redistributed. The presence of internal scaling factor is not taken into account in GR: function only of coordinate-like velocity of light is used as gravitational potential. In intrinsic spaces of matter changes of electromagnetic interaction distances are unobservable in GR in principle, while spatial inhomogeneity of this distance for uniform matter that takes place in background Euclidean space (and, consequently, spatial inhomogeneity of the values of its scaling factor) causes the curvature of matter intrinsic space. The one thing that points on it is the usage of the function of not the interaction frequency, but of common for all substances pseudo-vacuum coordinate-like velocity of light in GR as the gravitational potential.
Size of quantum length standard of the gas is decreasing in people world at the adiabatic increasing of this gas. This fact and the fact that change of distances of interaction of matter micro-objects (which determine size of its quantum length standard) is unobservable in GR in principle leads to increasing of corresponding to this gas gravi-quantum value of metrical volume of the vessel that contains this gas. Therefore, gravi-quantum metrical value of gas molar volume is decreasing not so fast as thermodynamic metrical value of its molar volume due to the presence of negative feedback [15; 17]. Such gravitational shrinkage of the size of quantum standard of length that takes place on the matter micro-objects level is analogous to relativistic shrinkage of the size of quantum standard of length along the direction of matter motion. However we cannot introduce the common space for GQ-FR of all matters because of the presence of the different intrinsic metrics of the space for each matter . Therefore, not gravi-quantum but thermodynamic metrical value of matter molar volume is used in the GR and in people’s world. In analogy to quantum clock, quantum and any other length standards can be used in GT-FR of people world only due to stability of their length when values of temperature and pressure remain constant. The least influenced by temperature and pressure are only the atomic standards of length that are based on the stability of frequencies of emission radiations. According to all of this, in RGTD, the same as in GR, it is rational to use only the common for all matters intrinsic space of GT-FR. And, that is why fG, fI and vl should be considered as the parameters that are not identical, but equivalent to pseudo-vacuum coordinate-like velocity of light vcv of GR. The usage of the common for the whole gravitationally-bonded matter thermodynamic time that is counted by standard atomic clock (instead of conventional gravi-quantum times, which flow rate is different for different matters and in different points of the space, and which are counted by their hypothetical quantum clock) is quite rational. It allows avoiding the necessity of transformation of time within the whole matter that is in the sate of RGTD-equilibrium. The possibility and necessity of this is due to the existence of closed system of all self-consistent pairs of additive one to another intensive and extensive parameters of matter when it is in the state of RGTD equilibrium. Existence of such closed system is revealed in the fulfillment of the Le Chatelier-Braun principle in all RGTD-processes.
In contrast to gravitational potentials and external scaling factors used in GR, RGTD-values of gravitational potentials and internal scaling factors are not equal for different contacting matters. Only spatial gradients of the logarithms of frequency fG of intranuclear and fI of electromagnetic interaction in all matters (they are identical to gravitational field strength), as well as spatial gradients of the logarithms of internal scaling factor NI, are mutually equal in the same world point. These spatial gradients of logarithms fG (gradlnfG=gradln(vl/c)≡ gradln(vcv/c)) for all matters are identical to the gravitational field strength in this point. The presence of identical spatial gradients in the same point of space justifies the usage in GR of the conventional pseudo-vacuum velocity of light vcv instead of intranuclear frequency of interaction fG. Related to it problems appear in GR only in the process of “stitching” of the solutions of equations of gravitational field for different matters. And this is related also to their stitching with fictive solutions for physically unreal absolutely empty space (spatially inhomogeneous pseudo-vacuum) . So, differential equations of GR gravitational field are definitely determine only the gradients of potentials and not the gauge transformed potentials of gravitational field themselves. However, in non-empty space they principally allow to switch from vcv to fG, fI and vcm And, therefore, these problems are solvable in GR. It is necessary and enough to determine (from equations of thermodynamics) the values of fI0 and vcm0 only in any single point of matter that is in the equilibrium RGTD-state. Then the spatial distributions of fI and vcm in any matter can be determined with the help of the solutions of GR equations. It is necessary to use correspondent vcm0 and fI0 values of coordinate-like velocity of light vcv0 and the known dependency of vcm on fI or on correspondent to fI thermodynamic parameters of matter.
Decreasing of the wave length of radiation in quasi-equilibrium compressed gas (proton-electron plasma) is practically completely compensated by decreasing of velocity of radiation propagation in it. This is also confirmed by the fact that emission radiation frequencies practically do not depend on thermodynamic parameters of matter.
However, such total compensation is absent at non-equilibrium state of ionized gas of quasars, situated in strong electromagnetic field (very saturated by radiation). Due to this and due to the proximity of the photosphere of shell-like quasars to the singular sphere they have the big gravitational redshift of the wavelength of emission radiation.
In contrast to “cooling down” stars, supernovae are heating up and, therefore, not contracting but catastrophically expanding due to annihilation of matter and antimatter [16; 19]. Instead of undercompensation of gravitational shift of radiation spectrum its thermodynamic overcompensation takes place – as a result, not red but blue gravithermodynamic shift of this spectrum takes place. Decreasing of quantum length standard (increasing of NI) that is not completely compensated by the decreasing of velocity vcm of interaction propagation causes not only the increasing of the frequency of electromagnetic interactions fI=NIvcm/c≠const for the supernovae, but also increasing of the frequencies of emission radiation ν=ν0NIvcm/NI0c≠const. Therefore, energy of ionized rarefied gas of the dropped supernovae shells, as well as non-Doppler values of its emission radiation spectrum, should be increasing along with increasing of pressure in the outer space at the advancing to cosmological past. Actual value of red shift of supernovae radiation spectrum is substantially lower than its theoretical value, determined by Hubble relation, due to the presence of such negative feedback. So the presence of dark energy in the Universe is not necessary.
Obviously in GR gravitational field equations not strictly thermodynamic value of matter molar volume is mainly used. Therefore, additional coordinates transformation is required for the transition from used in GR local intrinsic FRs of matter and from similar to them GQ-FRs to GT-FRs of people’s world. Only in this case the curvature of intrinsic spaces of matter is determined only by spatially inhomogeneous relativistic shrinkage of radial intervals and by radial delay in gauge evolution of matter self-contracting in CFREU (by gravi-evolutionary “deformation” of its micro-objects).
Internal contradictions in the theory of relativity and the main differences between the theory of relativity and relativistic gravithermodynamics.
Below is the list of facts that are internal contradictions in GR and SR:
1. The necessity in use of proper time (instead of classical absolute time) of moving matter, rate of which is determined by the rates of quantum processes in matter, is declared in SR. However, standard atomic or quartz clock is used instead of quantum clock of this matter. The rate of standard atomic or quartz clock, in contrast to the rate of quantum clock, is proportional not to the time standard, but to the used in them length standard. And, therefore, their time count, in contrast to quantum clock, does not depend or dismissively weakly depend on coordinate-like velocity of light and, therefore, on correspondent to it thermodynamic parameters of matter. Thus, the influence of pressure and temperature on relativistic dilation of proper quantum time of matter is not taken into account in the process of non-comfort motion of this matter that is accompanied by the appearance of internal stresses and elastic deformations in it. The influence of pressure and temperature in matter on conformal-relativistic (non-elastic) shrinkage of coordinate intervals in matter is also not taken into account. Exactly this shrinkage is responsible for the origin in observer’s FR of the gravitationally-kinematic curvature of the part of its intrinsic space filled by “non-comfort” moving (accelerating or rotating) matter. This leads not only to the unsuitability of SR transformations of increments of coordinates and time for the transition from intrinsic FR of rotating matter to observer FR (Ehrenfest paradox), but also to the separate problems in GR.
2. The fact that intrinsic STC of matter is formed directly by matter itself is declared in GR. In spite of this, values of components of STC metric tensor are considered to be independent from all properties of matter, located in concrete point of space. Thus, metric tensor in this point determines equal (not gauge mutually transformable, as it is expected) values of gravitational potentials for all possible thermodynamic states of matter Therefore, coordinate-like velocity of light, used in GR, is not a characteristic of matter, but, in fact, is a characteristic of the form of matter being – space, and can take any values that do not correspond to thermodynamic matter parameters and to real velocities of propagation of electromagnetic waves in it. This leads to the necessity of using in GR the special differential operators for dependencies of matter energy and momentum on its physical parameters. It also leads to the need to replace very massive neutron stars, which have the topology of a hollow body in the background Euclidean space and mirror-symmetric inner space, fictional "black holes".
3. Influence of gravitation on matter, as well as influence of nonuniform motion on matter, causes not only spatial inhomogeneity of the gravi-quantum rates of proper time of matter. This influence also leads to inhomogeneous deformation of matter on the level of correspondent to its nucleons terminal outlets of the turns of the common spiral-wave formation of the Universe in both background intrinsic space of the observer and in background Euclidean space of CFREU . The principle of unobservability of such deformation in all matter intrinsic FRs remains valid in GR. However, there is some exception in GR for relativistic length shrinkage: it is considered as observable in all FRs, not comoving with moving matter. This leads to a false relativistic generalization of thermodynamics with Lorentz-invariant volume .
4. Changeability of values of interaction distances of matter micro-objects in thermodynamic processes (these values together with the velocity of propagation of interaction determine the frequency of interaction) is not taken into account in GR. This causes the fact that GR gravitational field equations correspond to FRs of STC, but not to GT-FR of all matters, to which RGTD equations correspond. This makes GR equations useable only for homogeneous matter.
The fact that vacuum (coordinate-like pseudo-vacuum) velocity of light is more privileged than true velocity of light in matter in SR and GR makes these theories more corresponding to unrealizable in principle – degenerate states of matter than to real states [15; 19]. The fact that relativistic time dilation, as well as gravitational potential (and integral equations of gravitational field in matter), are strictly independent from concrete values of any characteristics, of this matter denotes the excessive simplicity of SR and GR that causes the primitiveness of representation of objective reality by these theories. The “beauty” of these theories, related to their simplicity, does not correspond to, in fact, not very “beautiful” objective reality.
In spite of this, the most of the original positions and principles of SR and GR are saved in RGTD. The main distinguishing characteristics of RGTD are the following original positions and principles:
1. Physical vacuum is a continuous (structureless) substance that is not involved in motion and rests in CFREU. Matter micro-objects (elementary pseudo-particles) and electromagnetic waves are only the non-mechanically excited states of this substance .
2. RGTD-state of matter is the spatially inhomogeneous average statistical macrostate of this matter. This state is determined by statistical distribution of possibilities of various collective space-time microstates (Gibbs microscopic states) of the whole gravitationally bonded matter. Discrete changes of collective space-time microstate of matter take place at de Broglie frequency, which corresponds to the collection of all jointly moving objects of this matter, and propagate as the quanta of action with a superluminal phase velocity. This takes place instantly in FR, comoving with matter, because of the fact that propagation front of quantum of action (that is responsible for the change of collective space-time micro-state of matter) is identical to the propagation front of succeeding time instant of moving matter both in CFREU and in FR of each of the observers of its motion.
3. Transfer of phase changes of collective space-time microstate of matter, as well as of graviinertial field (gravitational field, removable by coordinates transformation) strength, at a superluminal velocity do not accompanied by the propagation of changes of electrical and magnetic field strengths in the matter and, so, not accompanied by energy transfer . Released intranuclear energy of matter transforms into kinetic energy of directed motion before matter is filled in with external energy transferred at velocity of sound. Therefore, despite of the change of its motion velocity, matter moves only inertially during this period of time. In fact, free fall of matter in graviinertial field takes place.
4. Any arbitrarily rarefied matter of cosmic vacuum should be considered as incoherent matter, which abides to the thermodynamic laws, in analogy to ideal gas of non-interacting molecules . Because of this, and also because of principal unattainability of the zero value of pressure in gas-dust matter of cosmosphere, it is inadmissible not to take into account gradual decreasing of pressure in cosmic vacuum at the distancing from compact matter. And, therefore, vacuum solutions of gravitational field equations are senseless.
5. In contrast to the velocity of propagation of real electromagnetic waves in matter, conventional gravi-baric velocity of light in homogeneous matter, which is not equal but only proportional to the pseudo-vacuum coordinate-like velocity of light in GR, does not depend on the frequency of these waves. Values of this velocity are equal in straight and opposite directions at propagation of radiation along the direction of matter motion. This is caused by the fact that motion inducts relativistic changes of refractive index of moving matter. These changes cause the fact that values of gravi-baric components of longitudinal and transversal values of refractive index are not similar. The values of longitudinal and transversal components of refractive index guarantee the correspondence of relativistic values of longitudinal and transversal components of gravi-baric velocity of light to generalized relativistic nonvacuum transformations of spatial coordinates, time and velocities .
6. Relativistic transformations of spatial coordinates and time of SR are the vacuum degeneration of generalized relativistic transformations . Relativistic shrinkage of coordinate increments (“coordinate intervals”) is conform-Lorentz in general case. And it depends not only on velocity of matter motion, but also on the pressure inside the matter. The fact that graviinertial field is originated in nonuniformly rectilinearly moving matter, as well as in rotating matter, causes the fact that unobservable in principle relativistic deformation of matter is gravitationally-kinematic, in fact. Relativistic time dilation in moving matter is also gravitationally-kinematic. Graviinertial field in GR can be considered as removable only conventionally. Spatial inhomogeneities of thermodynamic state and of observable (non-relativistic) deformation of moving matter that correspond to coordinates transformation are not removed at this transformation. Differentiated tracking of the influence of removable and unremovable gravitational fields on spatial inhomogeneity of thermodynamic state of matter is impossible in GR in general case. Therefore, in GR, in contrast to RGTD, in general case gravitationally-relativistic dilation of physical processes in matter cannot be decomposed on multiplicative components that separately correspond to unremovable (external) and eliminable gravitational fields and to purely kinematic impact.
7. Intrinsic spaces of matter are metrically homogeneous (isometric) in principle. Gravitational, as well as relativistic, shrinkages of dimensions (length standards) and molar volumes are unobservable in these spaces. Gravitational curvature and comoving with moving object kinematic “curvature” of intrinsic space of motion observer are observable in these spaces, instead of these shrinkages. Therefore, relativistic transformations of SR are the transformations of the increments only of coordinates, but not of metrical intervals .
8. Covariance of equations of matter motion and state (and, in fact, covariance of the majority of physical laws) to the coordinates transformations takes place only for spaces of the GT-FRs of matter, namely, only for the spaces, in which matter deformations caused by relativistic and gravi-evolutional “deformations” of its micro-objects (correspondent to them spiral-wave formations) are unobservable in principle. Such deformations are “observable” in background Euclidean space  of CFREU (only in this space Universe can be homogeneous). A completely different formulation of the majority of nature laws, as well as other transformation of intensive and extensive parameters and characteristics of matter that correspond to this formulation and possibly different form of equations that determine interrelations between them are needed for intrinsic GQ-FRs of matter, in which not only evolutionary but also RGTD-“deformations” of its micro-objects (changes of their interaction distances) are unobservable in principle.
9. All thermodynamic parameters and characteristics of matter are invariant under both transpositional gravitational (spatio-temporal) and relativistic transformations of coordinates and time in principle. And, consequently, temperatures of phase transitions are the internal properties of matter of not only resting, but also moving bodies. The permanence (Lorentz-invariance) of observed thermodynamic state of moving matter when switch from its observation from any of IFR to the observation from any other IFR is provided by the calibration effect of classic inertial (hypothetic uniform) motion on the matter. It is guaranteed by the save of initial proportionality of observed rates of all physical processes to the rate of intrinsic time of moving matter. Ant the cause of all this is the self-consistency of all pairs of intensive and extensive thermodynamic parameters of matter that are complementary to each other. They form the self-enclosed RGTD-system.
10. Spatial inhomogeneity of RGTD-state of the whole gravitationally bonded matter (including extremely strongly rarefied incoherent matter of the outer space) is the cause of the presence of gravity. This inhomogeneity is reflected in homogeneous matter as certain spatial distribution of Gibbs free energy and of corresponding to this energy the nominal intensive parameter – relative average statistical value of the frequency of intra-atomic interactions (alternative to pseudo-vacuum coordinate-like velocity of light of GR). This field was originated due to the delay in the evolutionary process of decrease of intranuclear energy and the corresponding to it increasing of the Gibbs free RGTD-energy of matter. And it is the consequence of self-organization of collective macrostate of jointly moving matter that corresponds to the minimum of total (integral) value of the purely thermodynamic Gibbs free energy of this matter.
11. In relativistic thermodynamics, the same as in classical thermodynamics, all characteristic functions (potentials) of liquid and gaseous matter, which is under the influence of only all-round pressure and is in the state of both thermal and mechanical equilibriums, are determined only by two independent parameters  (while in GR there are three such parameters). In GR it is suggested that in the state of thermodynamic equilibrium not only the strictly concrete, but also different values of coordinate-like velocity of light of astronomical objects of different mass can correspond to all identical thermodynamic parameters of one and the same non-rigid (liquid or gaseous) matter within the whole volume of astronomical objects. In RGTD they can be different only for liquids and gases that are in the equilibrium thermodynamic state or for liquids that cover solid bodies and also for the solid (rigid) astronomical bodies themselves (the process of evolutionary decreasing of intranuclear energy of matter of such bodies is lagging). Moreover, in RGTD gravitational field equations define only equal gradients of logarithms of relative frequency of intranuclear (gravi-quantum) interactions for all matters. However, the values of this frequency themselves are not the same for different matters and are unambiguously determined by the difference of the molar mass of the matter from its critical value.
12. Bodies free fall in gravitational field – is an original realization of tendency of the whole gravitationally bonded matter to the minimum of the integral value not only of intranuclear energy, but also of thermodynamic Gibbs free energy. Bodies that fall independently accelerate in physically inhomogeneous space. In such way bodies transform their continuously released intranuclear energy into kinetic energy.
13. Removable gravitational (graviinertial) field, which is inducted by quasi-hyperbolic motion of matter during the process of its free fall, totally compensates external gravitational field. And, therefore, more dense particles cannot overtake less dense particles of incoherent matter in principle. Pressure in this matter, as well as relative frequency of intranuclear interactions, is spatially homogeneous (and this is reflected in the zero-gravity state). Matter free fall can be strictly inertial motion of matter only in hypothetic absolute vacuum. Therefore, matter free fall in atmosphere, as well as in the outer space, is only a quasi-inertial motion.
14. Not the total energy of matter, but only its inert intranuclear energy, which is equal to the sum of energies of nucleons and energies of intranuclear bonds and interactions, is equivalent to inert mass. Therefore, gravitational force that does not execute work is equal to the product of the Hamiltonian of only inert energy of the matter and the gradient of logarithm of relative frequency of intra-atomic interactions. By analogy, d’Alembert inertial pseudo-force is equal to the product of the Hamiltonian of matter intranuclear energy and the derivative of logarithm of relativistic time dilation along traversed path. And, consequently, there is no need in the proving of mutual equality of gravitational and inert masses of matter.
15. When the thermodynamic state of liquid or gaseous matter is equilibrium the gradients of conventional average value of intranuclear interactions are determined only by the gradients of its thermodynamic parameters. The frequency of the wave of one and the same emissive radiation remains the same in the whole (and even extremely rarefied) gas that is located at the long distance from the gravity center. And, therefore, declared in GR gravitational shift of the spectrum of emissive radiation of purely liquid-gaseous matter (which is strictly in thermodynamic equilibrium) of the astronomical object that does not have solid nucleus is impossible in principle. The shift of the maximum of heat radiation of this astronomical object is strictly determined only by the temperature of matter in its photosphere. Gravitational redshift of the spectrum of emission radiation can take place only for non-rigid (liquid or gaseous) matters that are in non-equilibrium thermodynamic state or for any solid (rigid) astronomical objects (the process of evolutionary decreasing of intranuclear energy of matter of which is always lagging). And, therefore, gravitational redshift of the spectrum of emission radiation is very negligible for the majority of astronomical objects. Mainly the Dopplerian widening of spectral lines takes place for them. The very significant gravitational redshift can be found only for the radiation of electron-proton plasma of quasar photosphere, where the lagging of the process of evolutionary decreasing of energy of protons is very big.
Gravitational field is the field of spatial inhomogeneity of thermodynamic state of matter and is not an independent substance (form of matter). Gravitational field cannot exist without matter, in principle, and, consequently, cannot have its own energy and own linear momentum that differs from energy and linear momentum of matter, which formed that field. Therefore, conservation of the sums of values of energy-momentum and moment of momentum together for matter and for gravitational field  is not necessary both in GR and in the RGTD. All bonds and interactions between matter structural elements have the same electromagnetic nature [16; 21], despite they all considerably differ one from another. And, therefore, gravitational field cannot be completely similar by its properties to electromagnetic field. Nature abhors uniformity. Nature “uses” new forms of bonds and interactions between matter structural elements on each new hierarchical level of self-organization of matter objects. However, for sure, all these forms are rather similar, because they are based on the same laws and principles of appropriateness. Statistical laws, which guarantee the correspondence of equations of RGTD-state of matter to the variational principles and, consequently, Le Chatelier-Braun principle, are the basis of gravitational and other RGTD properties of matter. Gravity forces are gravi-evolutionary pseudo-forces that force all matter objects to tend to spatially inhomogeneous collective equilibrium states with the maximum of the integral Gibbs free RGTD-energy and with the minimum of the integral thermodynamic Gibbs free energy of the whole gravitationally bonded matter. Because of this, GR gravitational field equations are, in fact, relativistic equations of spatially inhomogeneous RGTD-state of gauge-evolving matter (equations of RGTD) . And, therefore, gravity – is only the peculiar (sui generis) manifestation of electromagnetic nature of the matter on the appropriate hierarchical level of self-organization of matter objects. And, of course, there are no such objects as gravitons and gravitational waves that transfer energy (if, of course, moving matter itself is not considered as these waves).
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