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Preliminary Program 11-th International Gamow Conference-School Summer School "ASTRONOMY AND BEYOND: ASTROPHYSICS, COSMOLOGY AND GRAVITATION, COSMOMICROPHYSICS, RADIO-ASTRONOMY AND ASTROBIOLOGY" 22-28 August, 2011, Odessa, Ukraine
EVENTS: Monday, 22.08.2011 Arrival 09.00 ? 22.00 Registration of participants 20.00 ? 22.00 Evening session:
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Tuesday, 23.08.2011 06.05 09.00 09.00 11.00 13.00 13.15 14.30 15.50 16.20 18.00 19.00 19.55 21.00 06.06 09.00 11.00 11.30 13.00 14.30 16.30 18.30 19.53 ? ? ? ? ? ? ? ? ? ? 13.00 11.00 13.00 13.15 14.30 15.50 16.20 18.00 19.00 20.00 Sunrise Registration of participants Opening of the conference and Memorial Plenary session (3 reports) Photographing of participants Lunch Section sessions Coffee break Section sessions Dinner A.Shevchenko ? Guitar concert Sunset Welcome Party Wednesday, 24.08.2011 ? ? ? ? ? ? ? 11.00 11.30 13.00 14.30 16.00 22.00 19.30 Sunrise Plenary session (3 reports) Coffee break Plenary session (2 reports) Lunch Section sessions Shabo (vine sampling) Dinner Sunset
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Thursday, 25.08.2011 06.07 09.00 11.00 11.30 13.00 14.30 15.50 16.20 18.30 19.30 19.52 06.09 09.00 11.00 11.30 13.00 14.30 15.50 16.20 Close 18.30 19.50 20.00 ? ? ? ? ? ? ? ? ? 11.00 11.30 13.00 14.30 15.50 16.20 18.00 19.30 23.00 Sunrise Plenary session (3 reports) Coffee break Plenary session (2 reports) Lunch Section sessions Coffee break Section sessions Dinner Excursion, Opera theater, sea walk Sunset Friday, 26.08.2011 Sunrise ? 11.00 Plenary session (3 reports) ? 11.30 Coffee break ? 13.00 Plenary session (2 reports) ? 14.30 Lunch ? 15.50 Section sessions ? 16.20 Coffee break ? 18.00 Section sessions of Gamow summer school ? 19.30 Dinner Sunset ? 23.00 Conference Dinner Saturday, 27.08.2011 06.10 Discussions 19.48 06.11 Departure 19.46 Sunrise Sunset Sunday, 28.08.2011 Sunrise Sunset

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Scientific topics:
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23.08
14.30?18.00 - 14.30?18.00 - (2 )

24.08

25.08
14.30?18.00 -

26.08

Section 1. Cosmology, Cosmomicrophysics and Gravitation Section 2. Astrophysics Section 3. Radioastronomy Section 4. Sun, solar system and astrobiology Section 3-1. C ,

14.30?16.00 - (2 ) 14.30?16.00 - (1 )

14.30?18.00 - (2 ) 14.30?18.00 - (2 ) 14.30?18.00 - (1 )

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11-th International Gamow Summer School Conference-School "Astronomy and beyond: Astrophysics, Cosmology and Gravitation, Cosmomicrophysics, Radio-astronomy and Astrobiology"
(Ukraine, Odessa, Chernomorka, 22-28 August, 2011)

SCIENTIFIC PROGRAM
Monday, 22.08.2011
DAY OF ARRIVAL 09.00 ? 22.00 REGISTRATION OF PARTICIPANTS 20.00 ? 22.00 , -JENAM-2011 ? (.., ..), ( - ??)

Tuesday, 23.08.2011
Conference hall "Sovinyon"
09.00 ? 10.00 OPENING OF THE CONFERENCE AND MEMORIAL REPORT GREETING TALKS .. .. MEMORIAL REPORTS: 140- () : .. ( . ..) () ? 25 . .. ( . ..) "" ? -- XX : ? 20 . PLENARY PROGRAM 10.00 ? 13.00 PLENARY SESSION (4 reports ? 40 min) ? ..- A.D.Chernin (SAI, Moscow University) DARK ENERGY AND HUBBLE'S LAW: WHAT WAS DISCOVERED IN 1927-29?

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.D.Dolgov (INFN, Ferrara, Italy) STOCHASTIC BACKGROUND GRAVITATIONAL WAVES FORM PRIMORDIAL BLACK HOLES

OF

G.Tsarevsky (PRAO ASC LPI) PROJECT "RADIOASTRON" AND THE FUTURE OF SPACE RADIOASTRONOMY V.N.Melnikov (VNIIMS, Moscow) SCALAR FIELDS AND MULTIDIMENSIONAL MODELS IN GRAVITY AND COSMOLOGY

Wednesday, 24.08.2011
Cosmology, Gravitation and High Energy Physics Conference hall "Sovinyon"
09.00 ? 11.00 Plenary session (3 reports) ? .. G.Bisnovatyi-Kogan (IKI RAN) ACCRETION INTO BLACK HOLES WITH MAGNETIC FIELDS, AND RELATIVISTIC JETS A.A.Petrukhin (NRNU "MEPhI") THE PROBLEM OF ORIGIN OF VERY HIGH ENERGY COSMIC RAYS Zhuk A.I., Eingorn M.V. (ONU, Odessa) PROBLEMATIC ASPECTS OF KALUZAKLEIN MODELS 11.00 ? 11.30 Coffee break 11.30 ? 13.00 Plenary session (2 reports) .. ( ) S.G.Moiseenko ( )

Thursday, 25.08.2011
Cosmomicrophysics, Cosmology and Gravitation Conference hall "Sovinyon"
09.00 ? 11.00 Plenary session (3 reports) ? .. .. (, , ) RECENT RESULTS IN NEUTRINO PHYSICS .. .. (, ) .. ( ) ASTROPARTICLE PHYSICS 11.00 ? 11.30 Coffee break NONCOMMUTATIVE GEOMETRY IN

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11.30 ? 13.00 Plenary session (2 reports) .. (, ) . 35 .. (), .. (- , -) oEA-

Friday, 26.08.2011
Sun, solar system and astrobiology Conference hall "Sovinyon"
09.00 ? 11.00 Plenary session (3 reports) ? .. .., .. (- ) .., .. (Hydrometcenter of Russia) - ? ? ? .., .., .. ( ) ?? ? 23- 24- 11.00 ? 11.30 Coffee break 11.30 ? 13.00 Plenary session (2 reports) .., .., .. ( ) .. ( ) Discussion

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SECTION SESSIONS Section 1. Cosmomicrophysics, Cosmology and Gravitation Place: Conference hall "Sovinyon"

Tuesday, 23.08.2011
14.30 ? 15.50 Section sessions ? .. ., . ( , ) Irina N. Zavestovskaya (Lebedev Physical Institute of RAS, Moscow, Russia) OPERATOR TECHNIQUE SOLUTION OF THE KINETIC EQUATION Eingorn M.V., Zhuk A.I. (ONU, Odessa) WEAK-FIELD LIMIT IN f(R)-THEORIES OF GRAVITY WITH THREE AND MORE SPATIAL DIMENSIONS Kudinova A.V., Eingorn M.V., Zhuk A.I. (ONU, Odessa) MODIFIED NEWTON'S INVERSE SQUARE LAW AND ITS CONSEQUENCES IN THE RANDALLSUNDRUM MODEL WITH A SINGLE BRANE 15.50 ? 16.20 Coffee break 16.20 ? 18.00 Section sessions ( 15 .) ? .. Chopovsky A.V., Eingorn M.V., Zhuk A.I. (ONU, Odessa) THE NEGATIVE RESULT OF GRAVITATIONAL TESTS FOR KALUZA-KLEIN MODELS WITH SPHERICAL COMPACTIFICATION OF TWO EXTRA DIMENSIONS Kusevich A.E., Eingorn M.V., Zhuk A.I. (ONU, Odessa) AN IDEAL GAS OF BLACK STRINGS: TENSION FROM THE STANDARD GIBBS DISTRIBUTION POINT OF VIEW .. (, ) .., .., .. (, ) - .. (, )

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Thursday, 25.08.2011
Conference hall "Sovinyon" 14.30 ? 18.00 Section sessions ? .. .., .. (, ) .. (, ) , .. (, ) = 0 - kR .. .. (, ) ,



Nesterenko R. Pogosyan S. Pogosyan S. Skorkin V. (Institute for Nuclear Research RAS) : .., ..

..

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Section 2. Astrophysics
University Recreation Centre "Chernomorka" (2 )

Tuesday, 23.08.2011
14.30 ? 15.50 Section sessions (5 15 .) ? .. .A., .., .. NGC3227 2009 Shatsova R.B., Anisimova G.B. THE BRIGHT PART OF THE PERSEUS ARM V.Oknyanskij, B.Artamonov, E.Shimanovskaya, E.Koptelova PG 1115+080: NEW ANALYSIS OF LIGHTCURVES CONFIRMS OLD TIME DELAY RESULTS? Elena Panko, Alexei Pozanenko THE LARGE SCALE DISTRIBUTION OF GALAXIES IN IPN LOCALIZATIONS OF SHORT GAMMA-RAY BURSTS Tugay A.V., Vasylenko A.A. X-ray EMISSION IF GALAXIES WITHOUT ACTIVE NUCLEI 15.50 ? 16.20 Coffee break 16.20 ? 18.00 Section sessions ( 15 .) .. L.Ugolkova NUCLEA ACTIVITY OF SEEYFERT GALAXY NGC 7469 .., .. .., .., .. HII .., .., .. " " VSX J052807.9+725606 .., .. : , RU And Bukalov A.V. THE POSSIBLE NATURE OF THE NUCLEUS OF THE GALAXY AND AN ORIGIN OF A POSITRON STREAM AT THE GALACTIC CENTRE

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Section 3. Radioastronomy University Recreation Centre "Chernomorka" (2 )

Wednesday, 24.08.2011
14.30 ? 15.50 Section sessions ? .. .., .., .., .. 3 273 .., .., .. -600 A.Chuprikov RADIO STRUCTURE OF 1803+784 A.Chuprikov POLARIZATION PROPERTIES OF 3C273 M.I.Ryabov, A.L.Suharev WAVELET ANALYSIS OF PROCESS OF ACTIVITY OF A QUASAR 3273 IN RADIO-ULTRA VIOLET- X RAY

Thursday, 25.08.2011
14.30 ? 15.50 Section sessions ? .. M.I.Rjabov, A.L.Suharev, R.A.Sych, H.D.Aller, M.F.Aller WAVELET ANALYSIS ACTIVITY "CORE-JET" OF QUASARS AND BLAZARS IN CENTIMETRIC RADIO RANGE .., .., .. , ( 2010 ? 2011 .) .., .. . G.S.Bisnovatyi-Kogan, Yu.M.Krivosheyev SUBRELATIVISTIC JET HEATING MECHANISMS .. 15.50 - 16.20 Coffee break 16.20 - 18.00 Section sessions .., .., .., .., .., .., .., .., .. 347

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A.Chuprikov VLBI OBSERVATIONAL SESSION RAPL02. RESULTS OF POLARIZATION CALIBRATION OF THE DATA Miroshnichenko A.P. EVOLUTION FEATURES OF RADIO SOURCES WITH LOW-FREQUENCY STEEPNESS SPECTRA .., .., .., .., .., .., .., .., .. 3265 .., ., .., .., .. 102.5 : +14,1?...+80?,

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Section 4. Sun, solar system and astrobiology University Recreation Centre "Chernomorka" (1 )

Thursday, 24.08.2011
14.30 ? 16.00 Section sessions ( 15 ) ? .. Dorovskyy V.V., Melnik V.N., Konovalenko A.A., Rucker H.O. PECULIARITIES OF DECAMETER TYPE II SOLAR RADIO BURSTS ASSOCIATED WITH THE GEOEFFECTIVE CMEs .., .., .., .., .., .., . IIIb-III -2 .., .., .., .., .., .., ., . 7 2011 -2 .., .. : 13.09.2005 23:17 UT 01.01.2005 00:26 UT. .., .., .. ?-4?

Friday, 26.08.2011
University Recreation Centre "Chernomorka" (2 ) 14.30 ? 15.50 Section sessions ( 15 .) ? .. .., .., .., .. "-4" 2011 .. .., .., .., .., .., .., .., .., .. -22 .., .., ..

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.., .., .., .. NanoSail-D ? "" 15.50 ? 16.20 Coffee break 16.20 ? 18.00 Section sessions ( 15 ) .., .., ., .., ., .-., ., .., ., ., ., .. .., .., .., .., .., .. 22P/KOPFF, 81P/WILD, /2006 W3 (CHRISTENSEN), /2009 K5 (MCNAUGHT) ..

Bukalov A.V. PARAMETERS OF SPACE, BIOSPHERE OF THE EARTH AND ANTHROPIC PRINCIPLE

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, ( + 5-10 .)
University Recreation Centre "Chernomorka" (1 )

Thursday, 25.08.2011
14.30 ? 18.00 Section sessions ? .. .., .., .., .., .., .. .., .., .., .., .., .., .., .. .., .., .., .. .., .., .. .., .., .., .., .., .., .., .. .., .., .., .., .., .., .., .. (RADC) .., .., .., .., .., .. .., .., .., .., .., .., .., .., .., .., .., .., .., .., .. .., .., .., .. - .., .., .., .. , .. -- .., .. / .. ., ., ., ., ., . HD25354 .., .. EX HYA
Kirnichuk D., Chopyk.S.O GEODESIC LINES IN THE SPACES WITH ROTATION AND MOVEMENT OF THE STARS AT THE PERIPHERY OF GALAXIES?

.., .. GPS "-4"
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ABSTRACTS
11-th International Gamow Summer School Conference-School "Astronomy and beyond: Astrophysics, Cosmology and Gravitation, Cosmomicrophysics, Radio-astronomy and Astrobiology"
(Ukraine, Odessa, Chernomorka, 22-28 August, 2011)
140 ( ) ... .. . .. "" ? -- XX : .. . .. ??, 1904 , , ... - , .. .., .. .., .. .., . , .. .. .., 1920/21 - . .., ??. ? ?. .., , ??. 1904 1925 183 , 21 ? . , . .. .. . .. , . , ??, , , . . , , . .

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ACCRETION INTO BLACK HOLES WITH MAGNETIC FIELDS, AND RELATIVISTIC JETS G.Bisnovatyi-Kogan , Russia The problem of the formation of a large-scale magnetic field in the accretion disks around black holes is reconsidered, with account the non-uniform vertical structure of the disk. The high electrical conductivity of the outer layers of the disk prevents the outward diffusion of the magnetic field. The solution for a stationary state with a large magnetic field in the inner parts of the accretion disk, and strong vertical stratification is analyzed. Global solution of advective accretion disk structure around a black hole is constructed numerically. At high luminosity there is a continuous transition between the optically thick outer and optically thin inner disk regions. Models of accretion flows with large mass accretion rates are considered using a bridging formula for radiative losses at high and low effective optical depths. Contrary to the models neglecting advection, the global solutions have been found for all investigated range of accretion rates. The presence of the effectively optically thin regions in the innermost part of accretion disks results in a significant increase of the plasma temperature in those regions and this increase can be discriminated in observations in the form of the observed hard radiation tails. The temperature of the inner region is increasing with a growth of the angular momentum of the black hole, and may reach pair formation conditions for rotating black holes. Models of a magnetic jet collimation are constructed in a simplified approximation. DARK ENERGY AND HUBBLE'S LAW: WHAT WAS DISCOVERED IN 1927-29? A.D.Chernin Sternberg Astronomical Institute, Moscow University Neither Lema$\bf\hat{\imath}$tre nor Hubble discovered the global cosmological expansion predicted by Friedmann; it was done decades after them with observations at truly cosmological distances of more than 300-1000 Mpc. Lema$\bf\hat{\imath}$tre and Hubble studied receding motions of galaxies at local distances of less than 20-30 Mpc. They found empirically that these motions followed the (nearly) linear velocity-distance relation, known now as Hubble's law. According to Sandage, the cosmological interpretation and real physical sense of Hubble's law has been a mystery for 70 years. After the discovery of dark energy, we suggested that the dynamics of local expansion flows is dominated by omnipresent dark energy, and it is the dark energy ntigravity that can introduce the linear velocity-distance relation to the flows. If this is the case, Hubble's law discovered in 1927-29 was in fact the first observational manifestation of dark energy. STOCHASTIC BACKGROUND OF GRAVITATIONAL WAVES FROM PRIMORDIAL BLACK HOLES .D. Dolgov INFN, Ferrara, Italy It is assumed that in the early universe existed matter dominated stage due to nonrelativistic primordial black holes (PBH) with life-time shorter than the nucleosynthesis scale. Due to gravitational instability high density clumps of such PBH could be formed. Different processes of gravitational wave (GW) generation are studied. It is shown, in particular, that PBH binaries in these clusters could be effective sources of GWs. The matter dominated era could noticeably dilute GW from inflation. SCALAR FIELDS AND MULTIDIMENSIONAL MODELS IN GRAVITY AND COSMOLOGY Melnikov V.N. Center for Gravitation and Fundamental Metrology, VNIIMS, Russia Current basic problems of physics, gravitation and cosmology in particular, are analyzed. Special attention is paid to results in the theory of gravitation with a conformal scalar field, of the theory with extra dimensions and the problem of fundamental physical constants (FPC) variations. We use these theories for solving some basic problems of cosmology and BH physics, trying to find answers to such long-standing problems as singular or nonsingular initial states, creation of the Universe, creation of matter and its entropy, primary and present acceleration, cosmological constant (or vacuum), origin of inflation and specific scalar fields and their potentials necessary for their realization, isotropization and graceful exit problems, stability and nature of FPC, possible number of FPC and extra dimensions etc.
1. Staniukovich K.P., Melnikov V.N. // Hydrodynamics, Fields and Constants in the Theory of Gravitation, Energoatomizdat, Moscow, 1983. 2. Melnikov V.N. // Fields and Constants in the Theory of Gravitation, CBPF MO-02/02, Rio de Janeiro, 2002. 3. Melnikov V.N. // Multidimensional Classical and Quantum Cosmology and Gravitation. Exact Solutions and Variations of Constants." CBPF-NF-051/93, Rio de Janeiro, 1993; also in: Cosmology and Gravitation, ed. M. Novello, Edition Frontieres, Singapore, 1994, P. 147. 4. Melnikov V.N. // Multidimensional Cosmology and Gravitation, CBPF-MO-002/95, Rio de Janeiro, 1995; also in: Cosmology and Gravitation. II, ed. M. Novello, Edition Frontieres, Singapore, 1996, P. 465. 5. Melnikov. V.N. // Exact Solutions in Multidimensional Gravity and Cosmology III. CBPF-MO-03/02, Rio de Janeiro, 2002. 6. Melnikov V.N. // Proc.2000 NASA/JPL Conf. Fundamental Physics in Microgravity, NASA Document D21522, 2001, P. 4.1, Solvang, CA, USA.

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7. Melnikov V.N. // Gravity and Cosmology as Key Problems of the Millennium. Albert Einstein Century Int. Conf., AIP Conf. Proc., Eds. Jean-Michel Alimi, Andre Fuzfa, 2006, N 861, P. 109. 8. Melnikov V.N. // Variations of constants as a test of gravity, cosmology and unified models. Grav.Cosmol, 2007, V.13, N 2 (50), P. 81.

S.G.Moiseenko In my talk I plan to represent problems and advances in physics of core-collapse supernovae explosions. Explosion mechanisms of core-collpase supernovae will be discussed. Detailed attention will be given to the magnetorotational mechanism of explosion. Recent results of simulations of MR supernova will be discussed.

THE PROBLEM OF ORIGIN OF VERY HIGH ENERGY COSMIC RAYS A.A. Petrukhin National Research Nuclear University "MEPhI" Cosmic rays are very important source of information about processes in our Universe, about mechanism of cosmic particle acceleration and propagation. Two points of view about cosmic ray origin exist: galactic and extragalactic. At present, experimental data about cosmic ray flux characteristics do not give unambiguous answer about the origin of cosmic rays. In this lecture, various models of cosmic ray origin are considered, experimental possibilities to check these models are analyzed, and also existing approaches to interpretation of results of cosmic ray experiments are discussed. PROBLEMATIC ASPECTS OF KALUZA-KLEIN MODELS Zhuk A.I., Eingorn M.V. Department of Theoretical Physics and Astronomical Observatory Odessa I.I.Mechnikov National University We investigate classical gravitational tests for the Kaluza-Klein model with an arbitrary number of toroidal internal spaces. We obtain the parameterized postNewtonian (PPN) parameters for these models. The gravitational experiments lead to a strong restriction on the parameters of the model. The point-like massive source contradicts this restriction. The exact soliton solutions confirm this negative result. To avoid this problem, we consider the Kaluza-Klein model with spherical (of a radius a ) compactification of the internal space. The matter which corresponds to this ansatz can be simulated by a perfect fluid with the vacuum equation of state in the external space and an arbitrary equation of state with the parameter 1 in the internal space. We perturb the background ansatz by a point-like mass. and demonstrate that in the case 1 the perturbed metric coefficients have the Yukawa type corrections with respect to usual Newtonian gravitational potential. The inverse square law experiments restrict the parameters of the model: a / 1 6 ' 10-3 cm. In the Solar system the PPN parameter is equal to 1 with very high accuracy. Thus, our model satisfies the gravitational experiments (the deflection of light and the time delay of radar echoes) at the same level of accuracy as General Relativity. We demonstrate also that our background matter provides the stable compactification of the internal space in the case 1 > 0 . Namely this feature of the model provides agreement with the observations.

NONCOMMUTATIVE GEOMETRY IN ASTROPARTICLE PHYSICS ..

PROJECT "RADIOASTRON" AND THE FUTURE OF SPACE RADIOASTRONOMY Gregory Tsarevsky Astro Space Center, P. Lebedev Physical Institute, Russian Academy of Science, Moscow, Russia The International mission "RadioAstron" consisting of a very high orbit 10-m diameter space radio telescope, is going to be launched in July 2011. Its basic mode is a Space-Ground interferometer working with most sensitive ground radio telescopes to achieve better sensitivity. We believe that the extremely high angular resolution of this system would provide better understanding of the AGN central engine as well as numerous hot topics of modern astrophysics [1]. A future scientific and technical prospectives of this outstanding program is considered [2].
1. Kardashev N.S. // Experimental Astronomy, 1997, v. 7, p. 329 2. Kardashev N., Gvamichava A., Tsarevsky G., et al. // Acta Astronutica, 1979, v. 6, p. 175

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RECENT RESULTS IN NEUTRINO PHYSICS .. , , The current status of experimental and theoretical research in neutrino physics will be outlined. We will focus mainly on neutrino oscillation experiments, reviewing also results on neutrino direct mass and magnetic moment measurements. We will report on most recent results from OPERA, T2K, MINOS and some other experiments. .. . . , , . , - - - , ( ), ( ) . - - . "- ? -" , - ( " "). - 1012 0 ( - ). oEA- ..1, ..2 1 , -

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1. Bromm V., Larson R.B. // Ann. Rev. Astron. Astrophys., 2004. V. 42. P. 79. 2. Heger A., Woosley S. E. // Astrophys. J., 2002. V. 567. P. 532. 3. Heger A., Langer N., Woosley S. E. // Astrophys. J., 2000. V. 528. P. 368. 4. Chakrabarti S., Blitz L. // arXiv: 1007.1982v1 [astroph.GA] 12 Jul 2010.

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(Yp) (). , N(He)/N(H) .. , , 6 . W51 8 13 . HII , ; Yp = 25.96((+0.7)%. . .. . , , . , , . [1] , ( , , .. [2]). - [3] , . , . , ,

OPERATOR TECHNIQUE SOLUTION OF THE KINETIC EQUATION Irina N. Zavestovskaya Lebedev Physical Institute of RAS, Moscow, Russia, The distribution function for crystalline nucleous dimentions is found by exact analytical solution of classical kinetic equation in case of superfast temperature changing. The kinetic equation is solved taking into account physical features of crystallization at the superfast cooling realized in practice (existence of sufficiently large amount of overcritical nuclei and a plate form of the nucleis instead of spherical) and using operatory method which is usually applied to the Schrodinger equation. The result for distribution function allows us to calculate the finel crystalline nuclei dimention distribution if we know initial one. The everage number of particles in the crystalline nuclei and the relative volume change of crystalline phase were found as a function of thermodynamic paramaters of materials and cooling regime. Within the framework of the kinetic consideration of the proposed treatment regimes for amorphous phase formation can be described. The amorphization criterion is determined. WEAK-FIELD LIMIT IN f(R)-THEORIES OF GRAVITY WITH THREE AND MORE SPATIAL DIMENSIONS Eingorn M.V., Zhuk A.I. Department of Theoretical Physics and Astronomical Observatory Odessa National University named after I.I.Mechnikov We investigate the gravitational field of a point-like (delta-shaped) matter source in non-linear f(R)-theories of gravity in the case of an arbitrary number of spatial dimensions D 3 . If D = 3 , then we deal with an ordinary three-dimensional space. If D > 3 , then the

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space is multidimensional and we assume all extra spatial dimensions to undergo toroidal compactification. We consider the weak-field approximation with Minkowski and de Sitter background metrics. In both these cases point-like sources of the gravitational field demonstrate good agreement with experimental data only in the case of the ordinary three-dimensional ( D = 3 ) space. We generalize this result to the case of a finite perfect fluid with dust-like equations of state in external and internal spaces. This perfect fluid is assumed to be uniformly smeared over all extra dimensions and enclosed in a three-dimensional sphere. In the case of the ordinary three dimensional ( D = 3 ) space our formulas are useful for experimental constraints on different parameters of f(R)-models. MODIFIED NEWTON'S INVERSE SQUARE LAW AND ITS CONSEQUENCES IN THE RANDALLSUNDRUM MODEL WITH A SINGLE BRANE Kudinova A.V. 1, Eingorn M.V. 1,2, Zhuk A.I. 1,2 1 Department of Theoretical Physics 2 Astronomical Observatory Odessa National University named after I.I.Mechnikov Multidimensional brane world models with macroscopic and even infinite (non-compact) extra spatial dimensions seem to be one of the most attractive alternatives to multidimensional Kaluza-Klein models with microscopic finite (compact) extra dimensions. Obviously, these alternative models need experimental confirmation or refutation. We investigate the non-relativistic limit of the RandallSundrum (RS) model with a single brane, being one of the most popular multidimensional brane world models with a single infinite (non-compact) extra dimension. We apply both exact (in terms of Bessel functions) and approximate (in terms of the cubic correction) expressions for the potential of a delta-shaped material source, situated on the brane, to some geometric configurations, including the most important case of two interacting balls. We derive explicit formulas for the potential energy and the absolute value of the force of their gravitational interaction. Comparing our predictions with recent data of laboratory tests of the Newton's inverse square law at small distances, we obtain experimental constraints on parameters of the considered RS model. THE NEGATIVE RESULT OF GRAVITATIONAL TESTS FOR KALUZA-KLEIN MODELS WITH SPHERICAL COMPACTIFICATION OF TWO EXTRA DIMENSIONS Chopovsky A.V. , Eingorn M.V. , Zhuk A.I.
1 1 1,2 1,2

(the famous classical gravitational tests: the perihelion shift, the deflection of light, the time delay of radar echoes and PPN parameters) in the most important and physically reasonable case of a dust-like material source of the gravitational field. Now we generalize this unexpected result to the case of two extra dimensions compactified on a twodimensional sphere, representing the internal space. A tacit mechanism of compactification differs from the well-known Freund-Rubin mechanism. The background matter simulates a perfect fluid with the vacuum equation of state in the external space and the dust-like equation of state in the internal space. We conclude that this Kaluza-Klein model faces the same severe problem: obtained formulas for the light deflection, the time delay of radar echoes and the parameterized post-Newtonian parameter do not coincide with corresponding expressions of General Relativity and contradict astronomical observations. AN IDEAL GAS OF BLACK STRINGS: TENSION FROM THE STANDARD GIBBS DISTRIBUTION POINT OF VIEW Kusevich A.E. 1, Eingorn M.V. 2, Zhuk A.I. 2 1 Department of Experimental Physics 2 Department of Theoretical Physics and Astronomical Observatory Odessa National University named after I.I.Mechnikov The black string represents the extraordinary exact "soliton" solution of Einstein equations in fivedimensional space-time with a single finite (compact) extra spatial dimension. Its metrics describes the gravitational field of a non-dust-like matter source, possessing a rather specific energy-momentum tensor, including very strange relativistic negative tension. There are two main advantages of black strings. First of all, they are at the same level of agreement with classical gravitational tests as General Relativity. Secondly, black string equations of state do not violate the necessary condition of the internal space stabilization. However, there is no clear physical origin of tension, being the main disadvantage of black strings. We investigate this challenge from the point of view of the standard Gibbs distribution, generalizing this prevalent in statistical physics and thermodynamics distribution and its consequences to the multidimensional case. Using quantum mechanics, we find the discrete part of the free black string energy and consider an ideal gas of black strings, obtaining an explicit expression for tension and analyzing it. .. . , ,

Department of Theoretical Physics, 2 Astronomical Observatory Odessa National University named after I.I.Mechnikov In our recent paper we have shown that multidimensional Kaluza-Klein models with toroidal compactification of extra spatial dimensions face a severe problem. Namely, they contradict the experimental data

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1. 2. 3. 4. S.M. Carroll The Cosmological Constant. // arxiv: arstro-ph/0004075v2, 8 Apr 2000. .. .// , 2008, .178, 3. H. Wei Tension in the Recent Type Ia Supernovae Datasets //arXiv:0906.0828. .. . / .. // - ? ?. . 2011. .

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1. V. Gladush, M. Galadgyi. Some peculiarities of motion of neutral and charged test particles in the field of a spherically symmetric charged object in general relativity