FOUNDATIONS OF RELATIVISTIC GRAVITHERMODYNAMICS[1]
Danylchenko, Pavlo[2]
Research and Production Enterprise "GeoSystem" (Vinnytsia, Ukraine)
The cardinal difference between relativistic gravithermodynamics (RGTD) and general relativity (GR) is that in RGTD the extranuclear thermodynamic characteristics of matter are used in the tensor of energymomentum to describe only its quasiequilibrium motion. For the description of the inertial motion in RGTD only the hypothetical intranuclear gravithermodynamic characteristics of matter are used. Exactly this fact allows avoid the necessity of nonbarionic dark matter in the Universe in principle. 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 GR should be considered as equations of spatially inhomogeneous gravithermodynamic state of only utterly cooled down matter. This matter can only be the hypothetical substances such as ideal gas, ideal liquid and the matter of absolutely solid body. The real matter will be inevitably cooling down for infinite time and never will reach the state that is described by the equations of gravitational field of the GR. Only conditional identity of inertial mass of moving matter to its gravitational mass only by gravityquantum clock, which is located in the point, from which the matter started its inertial motion, and due to the usage of corrected value of gravitational constant in its pseudocentric intrinsic frame of reference of spatial coordinates and time, is justified. This is related to the equivalence of inertial mass of matter to the Hamiltonian of its inert free energy, while the gravitational mass of matter is equivalent to the Lagrangian of its ordinary internal energy. It was proved that total energy of matter of inertially moving body is equal in all global gravithermodynamic frames of references of spatial coordinates and time (GTFR) that are also inertially moving relatively to matter. The temporal invariance of not only the momentum but also of Lagrangian of ordinary internal energy and of equivalent to it gravitational mass of matter is justified. And that is precisely why there is the temporal invariance and a conformal 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. Exactly this fact allows avoid not only the twins paradox when twins are inertially moving but also the necessity of the dark energy in the Universe. It is also shown that the tensor of 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. The quantum equation of gravitational field have been found, the solutions of which set the spatial distribution of gravitational radius of matter in its every new gravithermodynamic state with the polynomial function with the next more high degree. The indicator of the degree of this function of continuously cooling down matter can successively take only integer and semiinteger values. That is why the process of cooling down of the whole RGTDbonded matter is the quantum process that is caused by its spontaneous transition to the polynomial function with more high value of degree and, therefore, to the next quantum collective state.
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, hidden variables, wave functions, quantum gravity, spiral waves, microobject, outer space, background regular space, photosphere, redshift, quasar, supernova.
PACS: 05.70.a, 04.40.b, 04.20.q
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

p. 
Preamble (from the author) 
3 
Introduction 
5 
1. Gravitational nature of the pressure in ideal gas and in conventional emptiness 
8 
2. Maximal possible velocity of matter 
10 
3. Physical essence of gravitational field 
10 
4. Thermodynamic nature of the majority of gravitational effects 
12 
5. Gravithermodynamic FR of people’s world 
13 
6. Inert free energy of matter 
18 
7. Generalization of RGTD equation 
19 
8. Nonidentity of inertial and gravitational masses 
30 
9. Gravitytemporal invariance of really metrical values of mechanical and thermodynamic parameters of matter 
32 
10. Equations of gravitational field of the RGTD 
35 
11. Equations of gravitational field of the galaxy 
40 
12. The condition of invariance of thermodynamic potentials and parameters with regard to the relativistic transformations 
48 
13. Generalized equations of thermodynamics 
68 
14. Physical and other thermodynamic characteristics of matter 
82 
15. The solutions of equations of gravitational field for cooled down to the limit and quantum quasiequilibrium cooling down gases 
86 
16. The comparison of reflection of physical reality in RGTD and in GR 
93 
17. Internal contradictions in the theory of relativity and the main differences between the theory of relativity and relativistic gravithermodynamics 
98 
Conclusion 
107 
Reference 
110 
Preamble (from the author)
Recently besides the epochal misunderstandings such as “Big Bang” of the Universe and “black holes” the two more not less significant misunderstandings appeared: “nonbarionic dark matter” and “dark energy”. This clearly testifies the presence of protracted crisis in theoretical physics. It gradually becomes the simple handicraft industry instead of creative reflection of reality. The gaps that were found in modern interpretations of very harmonious constructions of special (SR) and general (GR) relativities are started to be hushed up or “patched” via the introduction of new material entities (Kantian “thingsin themselves”) instead of reconsidering the physical entities of those theories themselves.
This crisis started right after the discovery of possibility to construct the relativistic theory of thermodynamics alternative to the theory of PlanckHasenöhrl by Heinrich Ott [Ott, 1963: 70] and independently from him by Heinrich Arsels [Arzelies, 1966]. Due to heavy debates on this question H. Arsels told about the “modern crisis of thermodynamics” (and not of SR). However the majority of physicists came to the conclusion about relativistic invariance of thermodynamics. And it is so indeed. Despite the principal possibility of relativistic dilatation of the intrinsic time of matter the matter that only inertially moves in the gravitational field is not affected in principle by this dilatation of intrinsic time. And it is guaranteed by more complex Lorentzconformal relativistic transformations of increments of spatial coordinates and time. These are why the tensor of energymomentum being based on the thermodynamic parameters and characteristics of matter can be formed only in frames of references of coordinates and time that is comoving with continuous matter. Unfortunately, the folk wisdom “the simplicity is worse than a theft” has been replaced in modern physics with the statement “everything genius can be only simple”.
The legitimacy of usage in the tensor of energymomentum of continuous matter of extranuclear (thus thermodynamic) parameters and characteristics instead of intranuclear was substantiated by Richard Tolman [Tolman, 1969], who proved the mutual consistency (correlation) of extranuclear and intranuclear parameters and characteristics of matter. In the quasiequilibrium state of matter the product of absolute temperature, that characterizes the intensity of extranuclear thermodynamic processes, and coordinate velocity of light, that characterizes the intranuclear state of matter, is the spatially homogenous magnitude. However, such correlation is absent for the noncontinuous matter of the galaxies and that is why the tensor of energymomentum of noncontinuous matter of the galaxy should be formed only based on relativistically noninvariant intranuclear parameters and characteristics of matter. It was for a reason that Albert Einstein himself had doubts that universal structure of tensor of energymomentum is possible and compared it with the low quality timber in comparison to metrical tensor, which he compared with elegant marble.
All these misunderstandings are caused by a distorted physical interpretation of the theory of relativity itself and by the not deep enough understanding of physical essence of different forms of such main physical concepts as space and time and also by the not having knowledge about physical processes hidden behind the mathematical model of spacetime continuum (STC). Both the revealed by Henri Poincaré physical nature of the curvature of intrinsic space of matter and the revealed by Hermann Weyl possibility of nonobservable in principle in people’s world gauge deformation of matter on the level of its microobjects and, consequently, of corresponding to it STC are de facto ignored. Moreover, not all people understand the united nation of thermodynamic and gravitational properties of matter, according to which the equations of gravitational field of GR are the equations of spatially inhomogeneous gravithermodynamic state of gauge evolving matter. The neglecting of the principal unrealizability of singularities in GR (taking into account the correspondence of zero value of coordinate velocity of light only to infinitely large values of absolute temperature and pressure), as well as the neglecting of possibility of selforganization by matter and antimatter of mirror symmetric configuration of intrinsic space, are responsible not only for the replacement of ultra massive hollow neutron stars by “black holes”, but also for the nonunderstanding of the nature of ultra high luminosity of quasars and supernovas. Nonperception of the fact that the Universe cannot be homogeneous in principle in intrinsic STCs of astronomical objects and the false identity (paralogism) of Etherington (that is based on the imaginary dilatation of intrinsic time of inertially moving far galaxies) are responsible for the fictive necessity of phantom “dark energy” in the Universe. Nonunderstanding of the fact that tensor of energymomentum should be formed not being based on the external thermodynamic characteristics, but namely being based on the intranuclear gravithermodynamic characteristics of noncontinuous matter, is responsible for the fictive necessity of phantom “nonbaryonic dark matter” in the Universe. The scientific research made by author, results of which are described in the proposed for consideration work, is dedicated to the justification of everything mentioned above.
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 [Binney & 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. Some authors [Gogberashvili & Kanatchikov, 2010] still continue the search for more weighty purely thermodynamic causes that are responsible for the curvature as well as for the physical inhomogeneity of intrinsic spaces of matter. Another authors [Jacobson, 1995; Verlinde, 2010] identify the gravity force with entropic force[3] not only based on thermodynamics, but also based on extraordinary properties of unreal “black holes”[4] (in astronomical observations the objects that are considered as “black holes” are indeed very massive neutron stars that have the topology of hollow body in background Euclidean space [Zeldovich & Grischuk, 1988] as well as mirror symmetry of intrinsic space). But, of course, gravity can be justified by just the selforganization (by the whole gravithermodynamically bonded matter) of spatially inhomogeneous gravithermodynamic states with gravitational outrunning of evolutionary selfcontraction of microobjets of matter in the bowels of astronomical objects [Poincaré, 1892; 1902; Sawyer, 1955]. And this is fundamentally possible due to the fact that the whole matter reaches the minimum of integral value of not only extranuclear Gibbs free energy, but also of intranuclear inert free energy. Therefore, phenomenological justification of the united nature of thermodynamic and gravitational properties of the matter [Danylchenko, 2008: 19; 2008a; 2009: 75; 2009a: 20/2; 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.
[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; 4th edition, revised and enlarged (publishing house “TVORY”, Vinnytsia, 2022); 5th edition, revised and enlarged, 2024.
[2] © Danylchenko, Pavlo, 2024, pavlo@vingeo.com.
[3] The gravitational pseudoforce that does not perform any work is caused by the nonconservation of the momentum in physically inhomogeneous space. Moments of virtual microobjects (quanta of energy), which are the objects of transfer between mutually interacting real microobjects, are increased in the process of their propagation to the gravitational attraction center and, vice versa, are decreased in the process of their propagation in the opposite direction.
[4] The impossibility of collapse of matter under the Schwarzschild sphere is quite obvious. In any moment of intrinsic time of matter it belongs only to infinitely far cosmological future and its radius in background Euclidean space is equal to zero [Danylchenko, 2004: 33; 2005a: 95; 2008b: 45]. And it is related to the fact that the simultaneity of events that take place in different points in cosmological time (but are simultaneous in SF of observer) is not fulfilled. According to mutual solution of equations of gravitational field of GR and equations of thermodynamics [Danylchenko, 2005b; 2008: 4] the tendency of coordinate velocity of light to zero is possible only when pressure and temperature tend to infinity. And, consequently, the real singular surface, on which coordinate velocity of light is very close to zero, can be only median surface. And it should separate external matter from internal antimatter. In internal space of hollow astronomical body the phenomenon of contraction of internal “Universe” takes place instead of the phenomenon of Universe expansion. And it means that in the internal space of hollow astronomical body the correspondent to antimatter divergent spiralwave formation (and not the convergent, as in external space) should be placed. Due to the fact that minimal Schwarzschild radius can take quite large values the mass of hollow neutron stars can be arbitrary large.
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