FOUNDATIONS OF RELATIVISTIC GRAVITHERMODYNAMICS[1]
Evolutionary selfcontraction of microobjects of lower layers of gravithermodynamically bonded matter outpaces the similar selfcontraction of its upper layers. This is the exact reason of the curvature of intrinsic space of matter. That is why gravitational field itself should be primarily considered as the field of spatial inhomogeneity of evolutionary decreasing of the size of matter microobjects in the background Euclidean space of expanding Universe. In correspondence to this the gravitational field itself is the field of spatial inhomogeneity of gravithermodynamic state of dense matter of compact astronomical objects, as well as of strongly rarefied gasdust matter of space vacuum. And, therefore, the gravitational field fundamentally cannot exist without matter. That is why it is not an independent form of matter. It is shown that equations of the gravitational field of General Relativity (GR) should be considered as equations of spatially inhomogeneous gravithermodynamic state of only utterly cooled down matter. This matter can only be the hypothetical substances such as ideal gas, ideal liquid and the matter of absolutely solid body. The real matter will be inevitably cooling down for infinite time and never will reach the state that is described by the equations of gravitational field of the GR. The equivalence of only inert free energy of matter (and not of the total internal energy) to gravitational and inert masses is justified. It was proved that total energy of matter of inertially moving body is equal in all frames of references of spatial coordinates and time that are moving relatively to matter. And that is precisely why there is a conform Lorentzinvariance of thermodynamic potentials and parameters in examined modification of transformations of the special theory of relativity (SR). Conformal relativistic transformations of increments of metrical spatial segments and metrical temporal intervals (instead of increments of coordinates and coordinate time of SR) were received. It is also shown that the tensor of energymomentum of matter (right side of the gravitational field equation) should be formed not being based on external thermodynamic parameters, but being based exactly on the intranuclear gravithermodynamic parameters. In this case the observed motion of astronomical objects of the galaxies is provided at arbitrary small density of mass of the matter on their periphery and, consequently, the presence of dark nonbaryonic matter in the Universe is unnecessary. Of course, bodies free fall in gravitational field is an original realization of their tendency to increase the evolutionary selfcontraction of microobjects of their matter, and the realization of the tendency of the whole gravitationally bonded inhomogeneous matter to the minimum of the integral values of its inert free energy and thermodynamic Gibbs free energy. Bodies that fall accelerate independently in spatially inhomogeneous medium of the outer space or atmosphere. Such bodies transform their continuously released intraatomic energy into kinetic energy. It is shown that in case of bodies’ free fall the gravitational deceleration of the rate of their intrinsic time is completely compensated by the motion due to isotropic allround conformal gauge selfcontraction of the size of falling bodies in the background Euclidean space of the Universe. Clocks that fall free are inertially moving and, therefore, continue to count time at the same rate as when they were in the state of rest. Similarly, the rate of time of astronomical body is not changed in the process of its motion in elliptical orbit. The dilatation of intrinsic time of distant galaxies is also absent, which points on the fact that Etherington identity does not correspond to reality. The fact that Hubble’s redshift is linearly dependent on transversal comoving distance instead of luminosity distance is justified. It is shown that mentioned above fact corresponds to astronomical observations. According to this the presence of dark energy in the Universe is also unnecessary. For the collective gravithermodynamic Gibbs microstates the connection between all thermodynamic potentials and parameters of matter have been found. This connection is realized with the help of several wave functions that can take arbitrary values with certain probability.
Keywords: gravithermodynamics, thermodynamics, gravity, gravitation, GR, SR, vacuum, inert free energy, Gibbs free energy, field, evolutionary and gravitational conformal gauge selfdeformation, allround isotropic conformal gauge selfcontraction of moving matter, collective spacetime microstate, Gibbs microstate, Lorentz conformal transformations, the principle of unobservability of the kinematic and gravitational selfcontraction of the size of matter, limit velocity of matter, coordinate velocity of light, internal scale factor, spiral waves, microobject, outer space, background regular space, photosphere, redshift, quasar, supernova.
But, it is similar to a building, one wing
of which is made of fine marble (left part of the equation),
but the other wing of which is built of low grade wood
(right side of equation). The phenomenological representation
of matter is, in fact, only a crude substitute for a representation
which would correspond to all known properties of matter.
Albert Einstein (Physics and reality)
Contents


Introduction 
3 
1. Gravitational nature of the pressure in ideal gas and in conventional emptiness 
5 
2. Maximal possible velocity of matter 
6 
3. Physical essence of gravitational field 
7 
4. Thermodynamic nature of the majority of gravitational effects 
9 
5. Gravithermodynamic FR of people’s world 
10 
6. Inert intranuclear energy of matter 
14 
7. Generalization of RTGD equation 
16 
8. Equations of gravitational field of the galaxy 
27 
9. The condition of invariance of thermodynamic potentials and parameters with regard to the relativistic transformations 
31 
10. Generalized equations of thermodynamics 
53 
11. The comparison of reflection of physical reality in RGTD and in GR 
70 
12. Internal contradictions in the theory of relativity and the main differences between the theory of relativity and relativistic gravithermodynamics 
74 
Conclusion 
83 
Reference 
85 
Introduction
Clausius's Hypothesis about opportunity of the heat death of the Universe (1865) and also the misconceptions about noninvariance 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. Selforganization 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 selforganization of different structural formations, the complexity of which grows with every new hierarchy level of selforganization of natural objects that form them. Relativistic generalization of thermodynamics with the invariant absolute temperature is currently considered as the most acceptable generalization [Van Kampen, 1968; Bazarov, 1964; 1991].
Thermodynamics was already used in this or that manner for analysis of the processes of formation of megascopic Universe objects [Antonov, 1962; LyndenBell & Kalnajs, 1972; Polyachenko & Fridman, 1976; 1984; Saslaw, 1968; 1969; 1970; 1985; Binney & Tremaine, 1987]. The main researches that should be highlighted: researches on gravitational plasma [Finney & Tremaine, 1987; Binney, 1993], researches based on the kinetic theory of rarefied gas [Zhdanov & Roldugin, 1998], and also the theory of spatiotemporal evolution of nonequilibrium thermodynamic systems [Olemskoy & Koplyk, 1995]. Recently, being based on the analysis of selforganization processes in nonequilibrium systems [Prigogine & Nicolis, 1977; Prigogine, 1985] and on the more wide usage of the methods of statistical physics, thermodynamics of selfgravitating systems achieved the quite significant success [Chavanis, 2002; 2005; Katz, 2003]. However thermodynamic and gravitational descriptions of the selforganization 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 [Danylchenko, 2008: 19; 2008a; 2009: 75; 2009a; 2010: 64; 2010a: 38; 2020: 5] 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 selfinducted 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 intraatomic physical processes in matter and, therefore, it inducts not only the curvature, but also physical inhomogeneity of intrinsic space of matter [Danylchenko, 1994a; 2004: 33; 2008b: 45]. 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 coordinatelike velocity of light in different points of this space [Möller, 1972].
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 quasihomogeneous cooling down is described by considered here modified tensor equations of GR – equations of relativistic gravithermodynamics (RGTD).
Increasing of coordinatelike 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 coordinatelike 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 – coordinatelike 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 gravitationallybounded 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 [Danylchenko, 2005b; 2008: 4], values of coordinatelike velocity of light are not vacuum values, but gravibaric 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 coordinatelike velocity of light. In the case of presence of both mechanical and thermal equilibriums in ideal liquid this pseudovacuum value of coordinatelike velocity of light is the same within the whole liquid, which selforganized its spatially inhomogeneous equilibrium state and gravitational field that corresponds to this state [Danylchenko, 2005b; 2008: 4]. This fact allows us to consider this vacuum value as gauge parameter, that interconnects spatial and temporal metrics and cannot be observed in gravityquantum intrinsic FRs (GQFRs) of matter and in people’s world FR in principle.
Conclusion
Gravitational field is the field of spatial inhomogeneity of gravithermodynamic 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 energymomentum and moment of momentum together for matter and for gravitational field [Brillouin, 1970, Logunov & Mestvirishvili, 1989] is not necessary both in GR and in the RGTD. All bonds and interactions between matter structural elements have the same electromagnetic nature [Danylchenko, 2004: 33; 2004a: 44; 2008b: 45], 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 selforganization 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 RGTDstate of matter to the variational principles and, consequently, Le ChatelierBraun principle, are the basis of gravitational and other RGTDproperties of matter. Gravity forces are evolutionarygravitational pseudoforces that force all matter objects to tend to spatially inhomogeneous collective equilibrium states with the minimums of the integral values inert free energy and thermodynamic Gibbs free energy of the whole RGTDbonded matter. Because of this, GR gravitational field equations are, in fact, relativistic equations of spatially inhomogeneous RGTDstate of conformallygauge evolving matter (equations of RGTD) [Danylchenko, 2008: 19; 2008a; 2009: 75; 2009a: 20/2; 2010: 64; 2010a: 38; 2020: 5]. And, therefore, gravity – is only the peculiar (sui generis) manifestation of electromagnetic nature of the matter on the appropriate hierarchical level of selforganization 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). Only the phase spiral waves of de Broglie – Schrödinger can be considered as the waves that transport only the change of collective phase (spatialtemporal) microstate of matter [Brillouin, 1970].
Not the total internal energy of matter, but its inert free energy is equivalent to gravitational and inert masses. Thermodynamic internal energy, which consists of the Lagrangian of ordinary internal rest energy (multiplicative component) and additive compensation of its multiplicative representation, is de facto the total energy of matter since it includes even the released kinetic energy of its motion. Thermodynamic internal energy of matter is equal in all FRs of bodies that move inertially relatively to it. And exactly this is the guarantee of Lorentzinvariance of all thermodynamic potentials and parameters of matter. Since matter motion is accompanied by the allsided conformallygauge selfcontraction of its size in background Euclidean space of the Universe the rate of the intrinsic time of inertially moving body is not dilated but, quite the contrary, remains invariant, despite the presence of gravitational decreasing of the rate of intrinsic time for nearby static objects. De facto the motion of the matter as well as its gravitational selfcontraction in background Euclidean space of the Universe leads to its advance over unobservable in people’s world evolutionary selfcontraction of the conventionally motionless matter in the Universe. That is why the release of kinetic energy is always accompanied by the decreasing of limit velocity of matter motion (that is identical to coordinate velocity of light of matter in GR) and the decreasing of its inert free energy.
The internal energy of matter is bonded in a different ways in different physical processes. That is why we have various free energies in different processes. Both the change of the inert free energy of matter (caused by its inertial motion) and its evolutionary decrease in CFREU do not directly influence the thermodynamic parameters of matter that are changed only in thermodynamic processes. That is why it is fundamentally unobservable in intrinsic FRs of matter in the similar way as evolutionary and caused by motion reduction of molar volume of matter is unobservable in commoving with expanding Universe FR. The gravitational reduction of molar volume of matter when approaching the gravitational attraction center is also unobservable directly in intrinsic FRs of matter. However, we still can say about its presence in Euclidean space of CFREU due to the presence of gravitational curvature of intrinsic space of matter. And we also can indirectly say about the presence of evolutionary selfcontraction of matter due to the presence of not only the process of Universe expansion in FR of people’s world, but also of correspondent to it global gravitationalevolutionary gradient lens (GGEGL). Moreover, not only evolutionary but also gravitational and kinematic deformations of microobjects of matter in background spaces (that form GGEGL) are isotropic. And, therefore, generally only the isotropic coordinates are used in RGTD. The evolutionary process of selfcontraction of correspondent to matter spiralwave formations forms not the ordinary but namely gradient global gravitational lens in expanding Universe [Danylchenko, 2009a: 20/1], which is revealed in the form of ordinary lens only along the world line of propagation of radiation. Gravityoptic power of gradient lens is smaller the closer are the observed objects. And it portrays the infinitely far objects of the Universe on the pseudo horizon of events that belongs only to the infinitely far cosmological past.
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[1] Reports in The allUkrainian seminar from theoretical and mathematical physics to 80 anniversary by professor A.V. Swidzynskiy in Lutsk (27.021.03.2009) and in The 4th Gamow international conference in Odessa (1723.08.2009). Abbreviated versions of the article were published in Proceedings of allUkrainian seminar from theoretical and mathematical physics to 80 anniversary by professor A.V. Swidzynskiy TMP’2009, Lutsk, February 2009, in Nauk. visn. Volyn’University, 6, 2010, in “Philosophy & Cosmology 2010”, 9, Poltava: Poltavskiy literator (2010) and publishing house “Nova knyga”, Vinnytsia, 2020; 3rd online edition, revised and enlarged.
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