Archive

Archive for the ‘3. Relativity and gravitation’ Category

May
06

Theory of conservative diffusion in classical and quantum systems

 Zahid Zakir [1]

Abstract

     In previous paper [1] conservative diffusion of light particles in a dilute medium of heavy particles was studied by analogue with Brownian motion. In the present paper the theory is formulated in more consistent “hydrodynamic” form by using a conservativity condition only, that mean energy of a light particle is conserved. As a model is taken diffusion of very cold light gas in warm heavy gas a time interval before relaxation when light gas remains cold. Unlike Lorentz’s gas, where thermal energies of light and heavy atoms are equal, here their thermal speeds are equal and this leads to the effects of conservativity similar to quantum effects. Such conservative diffusion is described by two equations – the continuity equation and the energy conservation condition, non-linear under the probability density. At introduction of a complex probability amplitude the equations linearized and turn to the Schrödinger equation. As a result, one must add not probability of alternatives, but probability amplitudes. A free pass length and corresponding momentum define an elementary phase volume and the diffusion coefficient. The predicting new quasi-quantum effects in classical systems are discussed. It is shown that the formalism of quantum mechanics describes the classical conservative diffusion with a constant diffusion coefficient and that quantum mechanics is a particular case of such diffusion in the vacuum where the elementary phase volume of free passage is equal to the Planck constant.

PACS: 02.50.Ey, 03.65.Ta , 05.40.Jc  

Key words: quantum mechanics, diffusion, Brownian motion, kinetic theory of gases

Vol. 9, No 1, p. 18 –32, v1,    6 May 2014

Online: TPAC: 4874-036 v1,   6 May 2014;   DOI: 10.9751/TPAC.4874-036


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

      zahidzakir@theor-phys.org

May
15

The closed model of the universe with relativistic redshift

 Zahid Zakir [1]

Abstract

     Starting from the relativistic dynamics of homogeneous expanding ball, a relativistic evolution equation for the closed model of the Universe is formulated which correctly takes into account a relativistic time dilation of proper times due to different expansion speeds at different epochs. The hypersurface of simultaneity of the Universe is spherically-symmetric only in the rest frame of 3-sphere’s centre and, consequently, the evolution is described in world time t of this frame of reference. This relativistic evolution equation coincided with Einstein’s equation for a 3-sphere expanding in 4-space (without dark energy) and has a simple exact solution. There is a relativistic redshift leading to new relation of redshift with the scale factor which then gives new “luminosity-redshift” relation well describing the data for Type 1а supernovae at admissible parameters. By using the initial data – present radius and expansion speed – other properties and evolution of the Universe are predicted. The model predicts that the observing baryon density is one third of total matter density and remaining two third is dark matter density. The accounting of stasis effects slightly changes the parameters only.

  PACS04.20.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, galaxy clusters, dark matter, dark energy  

Vol. 8, No 2, p. 24 – 36, v1,               15 May 2013

Online: TPAC: 4518-030 v1,             15 May 2013; DOI: 10.9751/TPAC.4518-030


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

      zahidzakir@theor-phys.org

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

Apr
15

The frequency and intensity stasis effects for radiation crossed galaxy clusters.

2. Isotropy and anisotropy of CMB

 Zahid Zakir [1]

Abstract

     In the previous two papers it has been studied a new class of general relativistic effects – the frequency and intensity stasis of radiation crossing gravitationally-bound regions (GBRs), such as galaxy clusters, due to switching out from the cosmological expansion flow. In the present paper the theory of stasis effects is applied to cosmic microwave background (CMB). For a part of CMB crossing a cluster these effects lead to the stasis of its temperature and «heating» w.r.t. a normally expanded flow outside the cluster. As a result, instead of former paradigm about almost sterile propagation of CMB from the recombination epoch, in fact, general relativity and cosmological principle lead to the opposite picture. Mixing of flows of relic photons, repitedly isolated many times from expansion flow in GBRs along their path, sufficienly changes the physical characteristics of CMB, particularly, leads to its isotropy and loss of earlier times perturbations. The observing anisotropy follows from the stasis effects at crossing of multiple layers of clusters at our nearest environment.

PACS: 98.80.Es, 97.60.Bw, 98.65.Cw, 98.62.Py, 98.62.Ck, 98.62.Qz, 98.80.Jk, 98.70.Vc

Key words: cosmology, galaxy clusters, gravitation, background radiation, anisotropy  

Vol. 8, No 1, p. 16 –23, v1,  15 April 2013

Online: TPAC: 4488-029 v1,   15 April 2013; DOI: 10.9751/TPAC.4488-029


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

      zahidzakir@theor-phys.org

 

Apr
15

 The frequency and intensity stasis effects for radiation crossed galaxy clusters.

1. Localized sources.

 Zahid Zakir [1]

Abstract

     In the previous paper it has been proposed and preliminary studied a new class of general relativistic effects following from switching out of radiation from the cosmological expansion flow at crossing the largest gravitationally-bound regions, such as galaxy clusters. In the present paper more consistent theory of such stasis effects is formulated and its observational consequences are considered, particularly, in this first part of paper the corrections to observational data for Type 1а supernovae are presented. Preservation of frequency and intensity of radiation at crossing large number of clusters leads to sufficient decreasing of observable redshifts z and higher apparent luminosities of sources. Only normal redshifts z’ of photons not crossed clusters, which give true distances exceeding the distances following from z, are directly related with the scale factor. The effects increase for distant objects because of smaller inter-cluster distances at early epochs. The existence of the stasis effects for radiation leads not only to new and more exact data analysis methods in extragalactic astrophysics and cosmology, but also to the revising of distance scales and properties of objects all classes.

PACS: 98.80.Es, 97.60.Bw, 98.65.Cw, 98.62.Py, 98.62.Ck, 98.62.Qz, 98.80.Jk

Key words: cosmology, gravitation, galaxy clusters, supernovae, redshift 

Vol. 8, No 1, p. 7 –15, v1,  15 April 2013

Online: TPAC: 4488-028 v1,   15 April 2013; DOI: 10.9751/TPAC.4488-028


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

      zahidzakir@theor-phys.org

 

Apr
15

Redshift stasis of photons at crossing the gravitationally-bound regions revises the supernovae data

 Zahid Zakir [1]

Abstract

     In gravitationally-bound regions (GBR), largest of which are galaxy clusters, metrics is averagely static and here objects, including radiation, do not participate at the cosmological expansion. In the paper the discovery of new observable effects for radiation crossed such regions – the redshift stasis and flux amplification – is reported. The stasis of wavelength appears as a blueshift with respect to a normally expanded flux and the stasis of distances between photons appears as a higher luminosity. Due to smaller inter-cluster distances at earlier epochs, the corrections to observing redshifts and magnitudes grow with distance. It is shown that the influence to the crossing radiation of switching off on expansion flow is significant and it may exceed up to two or three orders the ordinary gravitational effects of clusters. This sufficiently revises the estimations of characteristics of extragalactic objects and the confrontation with observations of cosmological models becomes correct only at accounting of these stasis effects. The stasis effects sufficiently change temperature of cosmic microwave background and its anisotropy also and lead to new blueshift effects, which particularly may appear in observations as a “dark flow”.

PACS: 98.80.Es, 97.60.Bw, 98.65.Cw, 98.62.Py, 98.62.Ck, 98.62.Qz, 98.80.Jk, 98.70.Vc

Key words: cosmology, gravitation, galaxy clusters, supernovae, redshift, background radiation

Vol. 8, No 1, p. 1 – 6, v2,  15 April 2013

Online: TPAC: 4488-027 v1,   15 April 2013; DOI: 10.9751/TPAC.4488-027


[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

Mar
23

On the theory of relativistic collapse and relativistic explosion.

1. Collapse without horizon and formation of frozars.

Zahid Zakir [1]

Abstract

        In general relativity (GR) the surface of a spherical object as an extended body is defined on hypersurfaces of simultaneity t=const and the proper time on the object’s surface at any moment is strongly related to the finite world time moment t (astronomical epoch). At any finite t this proper time moment always is less than its value at which the surface would cross the gravitational radius in the Newtonian theory. It is shown that in GR, as the surface closely approaches the gravitational radius, the proper times rapidly freeze (in terms of t) firstly at the center, where the time delay is maximal, then at higher layers, and that the surface freezes after all layers beyond the gravitational radius. The freezing of all processes in entire volume means the practically stopping of the collapse also. Thus, in GR there is a universal factor preventing the collapse – a strong gravitational dilation of the proper times, a fundamental physical phenomenon with which GR mainly differs from the Newtonian theory. For this reason in GR the horizons and singularities, as the Newtonian theory artifacts, do not arise and the black holes are forbidden. The collapse in GR leads to the formation of the frozars (frozen stars) the surface and all layers in entire volume of which are frozen. The worldlines of the particles in the star are timelike and almost parallel to the taxis and between each other. The formation of the frozars is shown for the standard idealized models of the collapse – a thin dust shell, a dust ball, a star of constant density and a star with ultrarelativistic matter. The astrophysical consequences of the theory of collapsed stars as frozars of GR are shortly discussed.

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

Key words: relativistic stars, collapse, frozars, black holes, horizon, singularity, time dilation

Vol. 7, No 1, p. 1 – 13, v1,  23 March 2012

Online: TPAC: 4100-024 v2,  28 September 2012; DOI: 10.9751/TPAC.4100-024


Nov
09

Four-index equations for gravitation and the gravitational energy-momentum tensor [1]

      Zahid Zakir [2]

Abstract

    A new treatment of the gravitational energy on the basis of 4-index gravitational equations is reviewed. The gravitational energy for the Schwarzschild field is considered.

PACS: 04.20.Cv, 04.20.Fy, 11.10.-z

Key words: gravitational energy, curvature tensor, vacuum energy

Vol. 5, No 2,  p. 22 – 25, v1,   9 November 2010

Online: TPAC: 3600-019 v2,  28 September 2012; DOI: 10.9751/TPAC.3600-019

[1] The preprint of the paper has been presented in 1999 (revised 2003): Zakir Z. arXiv:gr-qc/9906039

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

      zahidzakir@theor-phys.org