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Jun
05

Structure and evolution of a spherical dust star.

1. The modified Oppenheimer-Snyder solution

 Zahid Zakir [1]

Abstract

In the Oppenheimer-Snyder solution (OS) for the parabolic trajectory particle’s worldline r(t,R) in terms of world time t differs from its standard worldline in the Schwarzschild field outside and on the surface of the dust star. This is a consequence of the fact that the trajectory function r(t,R) were defined on the “homogeneity hypersurface”, when r = R at the zero initial moment of proper time in all layers and since these events are not simultaneous, the initial moments of the world time t(R) are nonzero. In view of the fact that the structure of the star at any moment means the determination of the positions of all particles on the hypersurface t=const., and the solution of the OS is used for checking more realistic models of stars, this incompleteness of the procedure for the transition to hypersurface t=const. leads to distortions of physical consequences other models too. A more consistent application of the OS method is proposed, where this problem does not arise. The modification consists in fixing the initial positions r=R for t(R)=0 and determining the shift of the proper time moments in different layers on the hypersurfaces t=const. from the condition of obtaining the standard trajectory function r(t,R). The pictures of particle trajectories of the dust star are presented, which clearly show the internal structure of the star at t=const. At large t, not only the surface asymptotically approaches the gravitational radius, but the world lines of particles in the inner layers also approach their asymptotes, rapidly becoming practically parallel to the world lines of particles at the center and on the surface. This shows that the frozen star picture refers not only to the surface, but also to the inner layers freezing at certain distances from the center.

   PACS: 04.20.Dg;  04.70.-s;  97.60.-s,  98.54.-h

   Keywords: relativistic stars, gravitational collapse, black holes, quark stars

 

Vol. 12, No 1, p. 1 – 16, v1,      June 5, 2017
Electron.: TPAC: 5200-041 v1,    June 5, 2017;             DOI:  10.9751/TPAC.6000-043


[1] Centre for Theoretical Physics and Astrophyics, Tashkent, Uzbekistan  zahidzakir@theor-phys.org

May
01

Diffusive mechanism for a small mass of composite particles and new perspectives for preon models 

 Zahid Zakir [1]

Abstract

   In the diffusion of cold light gas in warm heavy gas, initially and far before the relaxation, the thermal velocities of light and heavy atoms are the same order and the light gas remains cold, and mean energies of its particles are approximately conserved. The description of such conservative diffusion is analogous to the formalism of quantum mechanics, and quantum mechanics appears as a description of such diffusion of a particle in a physical vacuum, where the diffusion coefficient is proportional to the Planck constant inverse proportional to the mass. The growth of the diffusion flux in the localization of particles leads to an increase in the osmotic pressure, which reveals the “microscopic mechanism” of the uncertainty relations and allows us to identify cases where the prohibitions imposed by them can be circumvented, in particular, to solve the mass paradox for composite particles in the preon models. If two light particles (atoms) with different masses began to diffuse at distances much greater than the mean free path, then the diffusion mechanism prevents them from further joining and as more energy must be expended to form a composite particle, as smaller the final volume of localization. However, if these particles were initially located at a distance less than the mean free path and during a time shorter than the free pass time they formed a bound state (the atoms joined in the molecule), then this composite particle (molecule) diffuses as other light particles (atoms), but with a mass slightly less than the total mass of the initial particles.

PACS: 12.60.Rc, 12.60.Nz, 03.65.Ta, 05.30.Ch, 05.40.Jc

Keywords: composite models, technicolor, quantum mechanics, conservative diffusion

Vol. 11, No 1, p. 1 – 11, v1,     May 1, 2016
Electron.: TPAC: 5200-041 v1,    May 1, 2016    DOI: 10.9751/TPAC.5600-042

Mar
28

Finite quantum field theory with rotatory quantization and gravitational regularization

 Zahid Zakir [1]

Abstract

    At quantization of harmonic rotator, a rotational mode of planar oscillator, energy spectrum is linear on frequency and equidistant, but zero-point energy in ground state can not arise. This is in agreement with generalization of uncertainty relations to non-Hermitean canonical pairs. Quantization of waves at collective rotations of a chain of harmonic rotators allows one to model the fields with charge-conjugation and gauge symmetries. In quantum field theory (QFT) at quantization of rotational modes as harmonic rotators the observables of fields are normal ordered and zero-point energy and zero-point charge of vacuum do not arise. In this case frequencies of quanta are angular speeds of rotation of field vectors in real or field spaces and two signs of helicity correspond to a particle and an antiparticle. Photons with circular polarization and complex fields are examples of such fields, spin and isospins (charges) of particles can be related by their frequencies as angular momenta and helicities of the rotating field vectors. At rotational quantization of strings there are no zero-point energy of modes and here a conformal anomaly is absent, so spacetime dimensionality and gauge group are not fixed. In QFT the fields should be averaged in small cells of space and time, where distribution and evolution of fields are described classically, and field functions on borders of cells should be sewed. Then loop integrals are finite and the renormalized theories are invariant under reduction of the size of cells (a renormgroup with the cell regularization). The Planck scale cell is smallest because of freezing of proper times in a strong external gravitational field of the loop diagram with redshifting of frequencies up to zero. In the Standard Model and quantum gravity the loop contributions of fields, with exception of scalars, are small and the perturbation theory is convergent.

PACS: 03.65.Ge, 11.30.Er, 1130.Ly, 11.90. + t, 03.65.Ge, 03.70. + k, 11.10.Gh, 11.10.Hi, 11.15.Ha, 11.10.Ly, 12.20. – m, 11.25. – w, 12.10. – g,

Keywords: quantization, charge conjugation symmetry, harmonic rotator, quantum fields, vacuum energy, renormalization, regularization, strings, anomalies

Vol. 10, No 1, p. 1 – 40, v1,     March 28, 2015
Electron.: TPAC: 5200-040 v1,    March 28, 2015 DOI: 10.9751/TPAC.5200-040

Mar
28

Gravitationally frozen objects and relativistic explosion in general relativity: frozars, frozons and superbursts

 Zahid Zakir [1]

Abstract

 

In general relativity (GR) the worldline of a particle is unique and invariant, proper  time  and world time t are two parametrization of the same events on it only, that leads to a constraint for the proper time moments relating them by t. So, at contraction of a dust shell the proper times at finite t asymptotically freeze by no reaching a moment when the surface could cross the gravitational radius. Processes in entire volume of a star freeze at first at the center, then at higher layers, and at last the surface freezes outside the gravitational radius. Therefore in GR contraction leads to formation not black holes, but frozars (from “frozen star”) with the gravitationally frozen state of matter in entire volume, where the worldlines of particles are time-like everywhere, parallel to the t-axis and each other. Frozar formation in GR is shown for a thin dust shell, a dust ball, a star of uniform density and stars with ultrarelativistic matter. In real stars local temperatures in layers grow faster than temperature on the surface, and the last one grows on t exponentially fast. As high star’s mass, as high probability of that freezing occurs faster than warming up and the frozar will has time to be formed. But at lower masses, when the freezing does not enough fast, the warming up can stop contraction and can lead to explosion. During contraction a significant part of matter appear near the surface where in GR the physical volume sufficiently grows and energy of contraction is transformed to heat with transition of matter to the radiation dominated phase. If the star did not has time to be frozen, the part of ultrarelativistic matter and radiation leaves the star quickly, which appears as relativistic explosion, and the object will observed as relativistic supernova or hypernova. The observed lack of frozars of 2-4 solar mass and flat character of mass spectrum of more massive candidates to frozars confirm these predictions of the theory. the Big Bang and some explosions in astrophysics with large energy release probably are the cases of the relativistic explosion. In the frozar theory it appears a new GR phenomenon, the gravitational crystallization, defining structure of the most compact and massive objects in particle physics, astrophysics and cosmology. Gravitational radius of the system of few frozars sufficiently exceeds the radius of each of them and, therefore, at closing up they will not be able to merge and becomes frozen at distances larger their radii, forming a new state of matter – the gravitational crystal. Frozons, particles of the Planck energy, quantum fluctuations of which are frozen in their self gravitational field, also can not merge, i.e. for frozons there will be no interaction vertexes and they form only clusters and gravitational microcrystals. In astrophysics the supermassive frozen objects in the centers of star clusters, galaxies and quasars are probable gravitational supercrystals from frozars and ordinary matter. Relic frozons and frozar crystals could be the centers of inhomogeneities and also could be appear as a dark matter. If there is the backward contraction, the Universe as whole can be frozen also in the state of a global gravitational crystal which would stop the contraction.

PACS: 04.20.Dg;  04.70.-s;  97.60.-s,  98.54.-h

Keywords: relativistic stars, gravitational collapse, black holes, quark stars

Vol. 10, No 1, p. 41 – 67, v1,     March 28, 2015
Electron.: TPAC: 5200-041 v1,    March 28, 2015 DOI: 10.9751/TPAC.5200-040

May
15

The model of the closed Universe with relativistic effects of extra dimension

 Zahid Zakir [1]

Abstract

     In the standard general relativity (GR) a closed universe as a 3-sphere exists only at embedding into a real 4-space and a hypersurface of simultaneity of the universe is spherically-symmetric only in a global static frame where the center of the 3-sphere is rested. For this reason the evolution of the universe is described in a world time of this frame, where Einstein’s equations with homogeneous matter (without dark energy) have simple exact solutions. The radial speed of 3-sphere leads to the relativistic delay of proper times, which then leads to new expansion law and relativistic redshift. By using the initial data – present radius and velocity of expansion – other properties and evolution of the Universe are predicted and are in agreement with the data. As the result, from standard GR and observations follow that the Universe is closed, slowing down and the extra dimension probably really exist. The evolution is described for all epochs by taking into account pressure in earlier epochs. The nucleosynthesis and recombination occur at sufficiently smaller concentrations, but during sufficienly longer times. It is shown that the model is free on the cosmological problems of former approaches.

PACS:  04.20.Cv, 98.80.-k, 98.80.Jk 95.30.Sf, 97.60.Lf, 98.35.Jk, 98.54.-h, 98.80.-k, 04.60.-m  

Key words: cosmological models, redshift, supernovae, Big Bang, nucleosynthesis, recombination, cosmic microwave background, cosmological problems  

Vol. 8, No 2, p. 37 – 61, v1,               15 May 2013

Online: TPAC: 4518-031 v1,             15 May 2013; DOI: 10.9751/TPAC.4518-031


[1] Centre for Theoretical Physics and Astrophyics, Tashkent, Uzbekistan

zahidzakir@theor-phys.org

Jul
01

Dialogues about a fate of stars:

from black holes to frozars

Zahid Zakir [1]

Abstract

    Sagredo and Salviati – two friends of Galilee – almost 400 years ago in Europe disputed about motion of planets, after which the heliocentric system have been understood and accepted almost by all. Their descendants, who were friends too, almost 40 years ago in America, disputed about a gravitational collapse of stars, after which the black holes have been understood and accepted, but not by all. Among not accepted were one of friends and as a result recently their dialogue has been continued in Asia, but already about a choice between black holes and frozars. After that frozars began to be understood and accepted almost by all who had read record of this dialogue and for this reason it is presenting for wider public also.

PACS: 04.20.Dg; 04.70.-s; 97.60.-s, 98.54.-h

relativistic stars, collapse, black holes, supernova, gamma burst, quasars        

Vol. 7, No 2, p. 21 – 37, v1,  1 July 2012

Online: TPAC: 4200-026 v2,  28 September 2012; DOI: 10.9751/TPAC.4200-026


[1] Centre for Theoretical Physics and Astrophyics, Tashkent, Uzbekistan

      zahidzakir@theor-phys.org

Mar
23

On the theory of relativistic collapse and relativistic explosion.

2. Quasistable states as glowsars and bursts at recollapse.

Zahid Zakir [1]

Abstract

     At the gravitational collapse of a star the local temperatures in internal layers grow more rapidly than on surface, while the last one grows on world time exponentially. For this reason it is probable formation not a frozar, but an optimistic scenario of the collapse when matter of a star rapidly transfers into the radiation-dominated state with stabilization or further expansion (anticollapse). As a result, at stabilization the star can long on world time be in a hot phase (on local temperature). The semi-frozen relativistic objects in such quasistable phase release highly reddened quasirelict radiation and it is proposed to name this new class of objects as glowsars (glow star). Most of matter of glowsar concentrates near its surface in a radiation-dominated state. At defrosting of the glowsar its expansion at a final stage happens exponentially rapidly (the relativistic explosion) and the object is observed as the relativistic supernova or hypernova. Observable examples of the relativistic explosion, or anticollapse, are, perhaps, the Big Bang and some explosions in astrophysics with huge energy release, do not explained by known processes. Some idealized models and numerical simulations testify that at contracting of massive enough objects growing of pressure and temperature in internal layers can balance the gravitational pull and the explosive expansion is possible. The observable consequences of the predictions of GR about properties of the compact objects in glowsar state and the relativistic explosion are discussed.

PACS: 04.20.Dg; 04.70.-s; 97.60.-s, 98.54.-h

Key words: relativistic stars, collapse, frozars, glowsars, black holes, supernova, quasars

Vol. 7, No 1, p. 14 – 20, v1,  23 March 2012

Online: TPAC: 4100-025 v2,  28 September 2012; DOI: 10.9751/TPAC.4100-025


[1] Centre for Theoretical Physics and Astrophyics, Tashkent, Uzbekistan

      zahidzakir@theor-phys.org

Sep
14

Rotatory quantization of charge-conjugation symmetric systems.

3. Relativistic fields.

Zahid Zakir [1]

Abstract    

Quantum theory of complex fields with rotational modes based on a harmonic rotator model is constructed. For purely rotational modes the energy spectrum is equidistant, observables are automatically normal-ordered and there is no zero-point vacuum energy and zero-point charge. Frequencies of quanta are angular speeds of rotating field vectors (in real or field spaces). States of two signs of the helicity (particle-antiparticle) are related through the crossing symmetry. The well-known examples are photon field with circular polarization and complex fields. The spin and isospins of particles appear as related to their frequencies, representing angular momenta of rotations of field vectors with these frequencies. It is shown that the standard covariant perturbation theory is constructed in fact for description on the basis of harmonic rotators, where the recipe of transition from oscillatory to the rotatory representations of modes earlier it has been found empirically as normal-ordering of operators. The vacuum energy vanishes for free Hamiltonians and C-symmetric interactions.

PACS: 03.70. +k, 11.30.Er

Key words: quantization of fields, charge conjugation, parity, vacuum energy

Vol. 6, No 3, p. 48 – 63, v1,  14 December 2011

Online: TPAC: 4000-023 v2,  28 September 2012; DOI: 10.9751/TPAC.4000-023


[1] Centre for Theoretical Physics and Astrophyics, Tashkent, Uzbekistan

      zahidzakir@theor-phys.org

Sep
05

Rotatory quantization of charge-conjugation symmetric systems.

1. Harmonic oscillators

       Zahid Zakir [1]

Abstract    

In a system of a particle and antiparticle in the harmonic potential, represented as an oscillator with a complex generalized coordinate, there is a global U(1) symmetry and the charge conjugation (C) symmetry. It is shown that two pairs of ladder operators, introduced at the frequency decomposition of canonical variables, are not mutually charge-conjugate and that, therefore, their standard interpretation as operators of the charge-conjugate quanta breaks C-symmetry. Operator identities between bilinear products of the ladder operators are discovered, allowing expressing observables through charge-conjugate operators and it is correct to take into account C-symmetry. It is shown that these identities are maintained and at insert of the C-symmetric interactions. In a Lagrangian unsymmetrized and symmetrized orderings of complex conjugate operators of a momentum lead to different charge operators and are not equivalent at interaction with the gauge field. It is shown that due to C-symmetry conditions a zero-point charge does not arise in both orderings and in the first case a zero-point energy disappears also. The contribution of interaction with the gauge field and anharmonic potentials in higher orders of perturbation theory is considered. The same system also can be presented as a particle with positive and negative frequencies and, if to consider that a sign of mass of the particle coincides with a sign of its frequency, then the norm of negative frequency states remains positive.

PACS: 03.65.Ge, 11.30.Er, 1130.Ly, 11.90. +t

Key words: Hamiltonian dynamics, discrete symmetries, quantization

Vol. 6, No 2, p. 14 – 30, v1, 5 September 2011

Online: TPAC: 3900-021 v2, 28 September 2012; DOI: 10.9751/TPAC.3900-021

Download pdf 426 kb


[1] Centre for Theoretical Physics and Astrophyics, Tashkent, Uzbekistan

      zahidzakir@theor-phys.org

Sep
05

Rotatory quantization of charge-conjugation symmetric systems.

2. Harmonic and magneto-harmonic rotators

Zahid Zakir [1]

Abstract

     For soft rotators the lack of a radial component of velocity is a defining property and it allows to simplify quantization of harmonic and magneto-harmonic rotators. Operators of observables of soft rotators are normal ordered due to symmetries of the system, energy spectrum is linear under frequency and equidistant, and in the ground state there is no zero-point energy from rotational modes. It coincides with a generalization of the uncertainty relations for systems with non-hermitian canonical variables where the restrictions on fluctuations depend on state’s charge. Applications of the new formalism to quantization of waves at collective rotations of one-dimensional chain of harmonic rotators allows to model fields with charge-conjugation and gauge symmetries. For the rotating modes there is a crossing symmetry between states with opposite rotation directions, and arising of negative-frequency modes are positive-frequency states of antiquanta with replaced initial and final states. The commutators and causal correlators (propagators) of generalized coordinates of the harmonic rotator are derived.

PACS: 03.65.Ge, 11.30.Er, 1130.Ly, 11.90. + t

Key words: discrete symmetries, rotations, charge-conjugation symmetry, Landau levels, chain of rotators, propagators

Vol. 6, No 2, p. 31 – 47, v1,      5 September 2011

Online: TPAC: 3900-022 v2,  28 September 2012; DOI: 10.9751/TPAC.3900-022


[1] Centre for Theoretical Physics and Astrophyics, Tashkent, Uzbekistan

      zahidzakir@theor-phys.org