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FOUNDATIONS OF RELATIVISTIC GRAVITHERMODYNAMICS // Kiev: Library of Ukraine (ELIBRARY.COM.UA). Updated: 22.03.2019 . URL: https://elibrary.com.ua/m/articles/download/11192/3404 (date of access: 09.08.2024 )

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FOUNDATIONS OF RELATIVISTIC GRAVITHERMODYNAMICS (The full version of article) // Kiev: Library of Ukraine (ELIBRARY.COM.UA). Updated: 16.02.2020 . URL: https://elibrary.com.ua/m/articles/download/11192/3626 (date of access: 09.08.2024 )

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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.

**Synopsis**

*Clausius**'**s** **Hypothesis* about opportunity of t*he** **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 [9], and also the theory of spatio-temporal evolution of nonequilibrium thermodynamic systems [10]. Recently, being based on the analysis of self-organization processes in nonequilibrium systems [11] 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 [15] 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 [18].

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 [19], 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 [19]. 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 *ν** _{B}* and wave length

**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 [19]. 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

Absolute temperature is an intensive parameter that characterizes only the level of thermal internal energy ** U**(

**Inert intranuclear energy of matter**

Not the total energy of matter *U*_{GT}*= E+U*, but only the inert intranuclear energy

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 [15]. 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

**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 *f*_{N}*=η*_{m}**v****_{lb}**/

According to it, frequency of nucleons intranuclear interaction in GT-FR:

* *

*f*_{G}*=N*_{RE}*f*_{N}*=m/m*_{cr}** =**(

is equal to the division of the mass ** m** of one mole of matter by the value of this mass

*G***_{GT}**=

It is obvious that not only ** m_{cr}**,

Gibbs free RGTD-energy *G***_{GT}**, the same as Hamiltonian, is saved in the process of matter free fall. Moreover,

* *

*G***_{Nb}**=

*E***_{b}**=

Not only the molar mass itself ([1+** z**] times), but also its concentration in intrinsic space of the matter ([1+

While in all fast-flowing physical processes that are not accompanied by the performing of the work directed at the increasing of matter energy *U***_{GT}**, the Gibbs free RGTD-energy

Spatially inhomogeneous equilibrium RGTD-state of liquid and gaseous matter takes place in the case of fulfillment of the following: *G***_{GTj}**=(

In equations of GR gravitational field the thermodynamic enthalpy* **H***_{T}**=

* *

*G***_{Tg}**=

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 (*T***_{g}**≠

Internal energy ** U** of real gases and liquids depends on many pairs of their intensive (

* *

*U**= U_{id} +*

* *

*d U*=

where: ** T_{id}**=

“Ideal” component ** U_{id}** of internal energy is de facto identical to Helmholtz free energy

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 [2] that consists of the whole RGTD-bonded matter is indeed equivalent to enthalpy. Moreover, as it is shown further, ** A_{ρ}** parameter takes the same value in the whole space filled by quasi-equilibrium cooling down homogeneous matter (∂

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 *f***_{G}** 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 [34]:

** R=ρ**exp[–(

* *

** r=ρ**exp[–

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,

During matter free fall (*d S*=0,

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 *G*_{N}*/N**=**m _{cr}*

It should also be mentioned here that, according to GR and RGTD, the ideal gas (** pV**=

**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 *f***_{G}**=

In contrast to used in cosmology spatially inhomogeneous external scaling factor *N***_{E}**, which is the cause of the curvature of matter intrinsic space, internal scaling factor

**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 *f***_{G}** and

All the more so, separate contributions to gravitational potential of velocity of light in matter **v****_{cm}** and internal scaling factor

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 [15]. 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 *f***_{G}**,

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 *f***_{G}** of intranuclear and

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 *N***_{I}**) that is not completely compensated by the decreasing of velocity

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 [31]. 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 [28].

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 [16].

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 [32]. 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 [15]. 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 [33].

6. Relativistic transformations of spatial coordinates and time of SR are the vacuum degeneration of generalized relativistic transformations [33]. 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 [28].

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 [31] 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 [15] (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.

**Conclusion**

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 [35] 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) [15]. 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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