A POSSIBLE EXISTANCE OF A GRAVITATIONAL STRANGE PARALLEL UNIVERSE

trusciencetrutechnology@blogspot.com,Vol.2009, No.11, Dated: 17th November 2009
ON POSSIBLE EXISTENCE OF A GRAVITATIONAL STRANGE PARALLEL UNIVERSE AND REALIZATION OF OTHER FIELD STRENGTHS THROUGH THE STRANGE FIELD STRENGTH.
By Professor Kotcherlakota Lakshmi Narayana
(Retd. Prof. of Physics, SU)
17-11-10 Narasimha Ashram, Official Colony, Maharanipeta.P.O. Visakhapatnam-530002.
lakshminarayana.kotcherlakota@gmail.com: Mobile: 919491902867
ABSTRACT:
The strange field coupling with the gravitation from my model considerations and formulation has been derived to be a geometrical entity. Apart from it we have, of course, the strangeness characterization as per the elementary particle physics first enuniciated in SU(3) Unitary Symmetry. The state of matter created at RHIC does not support to the concept of ordinary colour neutral hadrons and implies the formation of a new state of dense matter. Results of LHC, a bonus of the New Year 2010, are awaited to thwart the current ideas of elementary particle physics. The present work surmises how one may replace the concept of physical entities in terms of purely gravitational strange strength of a parallel universe. Hence no one need be afraid of catastrophic consequence of Hadrons extremely energetic head-on collision of the LHC.
Keywords: Astrophysics, Particle Physics, strangeness, Mathematical Physics, conformon, RHIC, LHC, Cosmology, relativistic field equations, electric charge density, strange quark fluid energy density, quark fluid density, vacuum energy density Bag constant, magnetic monopole strength, Cosmod transformations.

INTRODUCTION:
The idea of textures like monopole, strings and strange fields etc generally thought as due to vacuum symmetry breaking or quantum field fluctuations in the early universe are being extensively investigated as well in order to explain the large- scale structures of the universe apart from other physical features of space-time geometries. String dust solutions of the Einstein Field Equations with spherical or static cylindrical symmetry have been described by Nevin [1] to obtain ‘thickened’ string in the sense of Stachel [2]. Earlier Letelier [3] has constructed a spherically symmetric star consisting of a perfect fluid core for 0≤ r≤ r0 surrounded by string dust for r₀ ≤ r <>r₁. He also gave a new model [4] of a cloud formed by massive strings in the reteam of General Relativity to describe Bianchi type I and Kantowski-Sachs type of cosmologies. It’s interesting that in the evolution of the universe it was suggested the strings to disappear and only particles would eventually remain.
The clouds of strings posses a proper energy density, with the particles attached to the strings. Strings are characterised by a string tension density. K. D. Krori et al [5] have studied this model of Letelier [4] for the case of Bianchi types II, VI0, VIII and IX. The study of cosmic strings has been suggested by Zeld’ovich [6] to give rise to perturbations leading to formation of Galaxies. Kibble [7] sought the possible existence of strings in a large net work structure of the early universe. Obviously they posses stress energy and are coupled with the gravitational field. Vilenkin [8], Gott [9] and Garfinkle [10] have studied the gravitational effects of the strings.
Surprisingly there is no direct evidence of the strings observed in the present day universe. Banerjee [11] studied the role of magnetic field for Bianchi type I string cosmological models. Ramesh Tikekar et al [12] have reported some exact solutions of String Cosmology in Bianchi III Space-Time with and without the electromagnetic field and they assert that when the parameter ‘a’ of the Bianchi type III metric is zero then the physically viable expanding Bianchi type I model in String cosmology persists.
The method to involve Bag Constant B=57MeV/fm3 in the field equations and to determine the energy density of strange quark stars as ρ =4E+14g/cm³ has been detailed by Aktas and Yilmaz [13]for the spherically symmetric space-time admitting one parameter group of conformal motions.
Why anisotropic and inhomogeneous cosmologies are are important? This question led to the formulation of less simplified cosmologies, which would give a satisfactory scenario of the universe and its evolution. Excellent review has been presented by Meisner, Thorn, and Wheeler [14] of these aspects of irregular starting of the universe, on consequent formation of galaxies and to explain certain anisotropy of the background microwave radiation. The study would undoubtedly sets the limits on the possible density and temperature irregularities that might have existed billions of years ago.Misner [15] gave an equation of state for the anisotropy energy density which enters the time diagonal component of the Einstein equations on equal footing along with matter energy density.
The anisotropy energy gets converted into thermal energy, resulting in possible universe of thermal radiation, which is characterized by blue shifted quanta moving along contracting axis and would emit red shifted frequency corresponding to a low energy distribution along other axes. Thus results in a large production of entropy. Destruction of anisotropy seems to be explained away by the processes of adiabatic cooling and viscous dissipation. The virtual quanta presence and the created particle-antiparticle, due to zero-point oscillations (vacuum fluctuations) would also have their energies blue or red shifted in frequencies by the influence of gravitational fields. It’s interesting to note that it is presumed that particle creation process normally uses the anisotropy energy. Inhomogeneous cosmology models involve the metric that has dependence on the space coordinates. Lamaitre [16], Tolman [17], Datt [18] have described models of spherical symmetry of this type and later by Bondi [19]. An alternate approach has been given by Khalatnikov and Lifshitz [20] who have sought to study the widest possible class of solutions near the neighbourhood of a singularity.
Misner [15] studied a more complex homogeneous anisotropic model of cosmology. The three parameters enunciated by him one corresponds to the general scale of the universe, and the other two prescribe the anisotropy. The scale parameter plays the role of time while the anisotropy parameters act as spatial coordinates. Many questions and ambiguities relating to this model were raised by Vladimirov, Mitskievich, Horsky in their book published in 1983.
The state of matter created at RHIC does not support to the concept of ordinary colour neutral hadrons and implies the formation of a new state of dense matter. [21]. Mansouri and Mohazzab [22] state that tunnelling rate in homogeneous and anisotropic cosmologies calculated by the two different methods, Viz. Euclidean and Hamiltonian approaches exhibits an exponentially decreasing probability for tunnelling as the anisotropy increases. Paul and Paul [23] presented details of anisotropic Bianchi-I universe with phantom fields and the cosmological constant. They state that recent astrophysical data obtained from high red shift surveys of Supernovae COBE to WMAP supports the idea that present universe is passing through an accelerating phase of expansion and emphasize the need of models with exotic fields, whose appearance may not be clear. The matter sector of Einstein’s Equations needs to be thus modified with new fields and perhaps new physics is to be explored. Alimohammadi [24] thought of an EOS ω = p/ρ =-1 as the so called phantom divide-line and for ω < -1 a phantom scalar field σ appears. For ω > -1 has the quintessence field consisting of a normal scalar field φ. Star models with Dark Energy discussed by R. Chan et al [25] has inner core as homogeneous with anisotropic pressure. The anisotropy in the pressure changes with M(r)/r with M(r) = 4*π*μ ₀ r^3/ 3 where μ = μ ₀=constant is the anisotropic fluid energy density and r is the radial coordinate.
The gauge theory approach to Quark-gluon Plasma has been studied by the present author and his student Miss A.M.Kulkarni in 1987 hinting at the concept of quark-gluon plasma described in terms of lattice point and hence abandoning of the concept of space-time continuum. Wilson introduced the lattice formalism. Gluon-gluon interaction is more colourful and sought to exhibit the flavour features according to SU (3) symmetry, flavours being Up, Down and Strangeness. The particle cosmology hence suggests possible 64 kinds of neutrinos which imply more flavour degrees of freedom to the quarks. The dense matter also has been thought as to lead to deconfinement of quarks from nucleons at sufficiently high energy, forming essentially quark conducting state, due to the dense packing. This is what is termed as a phase transition from an insulator state to a conductor state. The gauge invariance discovered as a remarkable property of Maxwell’s Equations of Electromagnetism asserts the photon as massless. But Quantum electrodynamics with Ward-Takahashi identities allows certain renormalizability. Quantum chromodynamics , GUTs, the supersymmetry and Super Gravity theories go several steps further to describe the marriage between particle matter physics and the space-time structures.
Originally in 1956 physicist Sakata suggested the three fundamental particles u,d,Λ to explain the occurrence in nature of the about 20 metastable mesons, baryons, anti-baryons, pseudo-scalar mesons and their resonance states. A unified description of the elementary particles has been thus given by Sakata. Zweig termed these three particles as Aces. Gellman-Ne’emann Scheme of eight fold (in the style of Buddhist philosophy) has been found to be more elegant with the completeness of the scheme, however challenged in 1974 with discovery of a new hadron. Present author and Miss. S. P.Shahane in the year 1978-1979 have completely worked out the SU (8) unitary symmetry problem for elementary particles classification and on page 86 of her post-graduate degree dissertation specifies the particle assignments. Also the Lie algebra of the Lorentz group infinitesimal operators which leave the space-time quadratic form invariant have been listed along with their structure bracket expressions. The analogy of these with the generators of angular momentum to describe the Dirac particle of Spin ½ has been given asserting why the Dirac field is invariant under the Lorentz transformations.
In other words, the strangeness concept seems to be only a feature introduced effectively, for the purpose of classification of elementary or the fundamental particles in the subject of Particle Physics and to explain the collision cross-section formulae of accelerator experimental investigations. What is its origin no one ever explicitly stated? The controversial role of strangeness in the spin structure of the nucleon as pointed out by E. Leader et al [26] arose from EMC experiments on polarized deep inelastic scattering of leptons on protons in 1988.
The strange field coupling with the gravitation from my model considerations and formulation has been derived to be a geometrical entity. Realization of the strange stars in terms of the General Theory of Relativity of gravitation and Einstein like relativistic field equations has been a long standing desire of the present author. The present article is one of a culminating work to this desire.
.
THE RELATIVISTIC FIELD EQUATIONS AND THE STRANGE STARS:
The Bianchi III type space-time metric has been considered with the object of realizing the nature of the strangeness property of the universe as a geometrical entity.
ds² = dt² – A²(t) dx² –B² (t) exp (-2*a*x) dy² - C²(t)dz²
where ‘a’ is a constant. A, B, and C are functions of time t only.
The energy momentum tensor for a cloud of string dust with both the magnetic and electric fields has been adopted. The quantity ρ_s is the strange quark fluid energy density, ρ = ρ_q + ρ_s+ B_c being the proper energy density for a cloud of strings. Ε is related to the elementary electrostatic charge I consider strange quark fluid energy density ρs and quark fluid density ρq and as well the vacuum energy density B_c (the Bag constant).
Setting A=B for Bianchi type III for which the parameter ‘a’ is non-zero, the Relativistic field equations according to my model are,
G ¹ ₁ = -1/2 h² - ε² /2 exp(-a*x)/A² ;
G ² ₂ = +1/2 h² - ε² /2 ex p(-a*x)/A² + 4*gs2 * a^2 *exp(-2*a*x)*[1-exp(2*a*x/A^3] ;
G ³ ₃ =- ε² /2 exp(-a*x)/A² + ρ_s x³ x ₃ ;
G ⁴ ₄ = + ε² /2 exp(-a*x)/A ² - ρ u ⁴ u ₄ ;
here gs2 is the square of gs i.e. the strength of the strange field coupling with gravitation. The h² expression is given by gm2*exp(1/A^2)/A^4 with gm2 as the square of the magnetic monopole strength gm. Here u are the fluid flow four- vector, x describe the direction of anisotropy, satisfy the with the conditions u ^μ u _μ = - x ^μ x _μ =1 and u ^μ x _μ =0.

The strange field coupling with the gravitation from my model considerations and formulation has been explicitly derived to be a geometrical entity. Apart from it we have, of course, the strangeness characterization as per the elementary particle physics first enunciated by Sakata and later asserted by Gellmann-Nee’man in their SU (3) unitary symmetry model. This strangeness is what is being extensively pondered upon in the literature for existence of strange stars (neutron stars or quark stars). To the present author’s knowledge no one has ever thought of gravitational strangeness. Thus possibly if one sticks to the string cosmology model then the strings need themselves to be gravitationally strange.
Cosmod transformations and concept of strangeness:
Strangeness has been thought by the present author in the context of classification and categorization of the Spin 2 massive mesons, and way back in 1970s asserted the possible existence of a second type [27,29a,29b,29c] of gravitational force. The Cosmod transformations of the universe one of ordinary universe of gravitons (with possible rest mass however negligibly small it may be) and the another of much more restricted, than the Hubble radius of the present universe has far reaching significance in the models of cosmologies.
A gauge-noninvariant scalar density theory with the object to get the hither to unknown inherent symmetry principle, has been taken as a clue to state that the mass difference of Spin 2 mesons observed in particle theory and almost vanishing rest mass of the graviton of theory of gravitation waves, have its origin in symmetry rather than in dynamics. Essentially, more caution has been made, to consider the mass difference of Spin 2 mesons of particle physics and graviton-like quanta. An imaginary quantum number iξ for Spin 2 particles gives rise to a one dimensional non-unitary transformation and which need not be conserved. The existence of this quantum number and violation of it in a specific way has been sought to provide some clues in the dynamics of Spin 2 particles.
The following transformation has been suggested by the present author for x and γ _{i k}
X==> x’= λ x,
γ _{i k} ==> γ’ _{i k}
(x’) = exp[ξΔ] λ α γ’ _{i k} (λ x)

where Δ is a parameter different for the different Spin 2 particles, value of α chosen appropriately and
Δ ==> Δ’ = Δ if ξ = ξ ‘ .
The transformation for γ _{i k} involves both a gauge transformation and a scale transformation and has been termed by the present author as the “COSMOD TRANSFORMATION”. The integral of the Lagrangian L given by Pauli and Fierz [28] involves certain constants the values [29] which do not subscribe or effect the Cosmod transformations. The Lagrangian is useful to define the Cosmod transformations yielding that λ =exp [-ξΔ] and thus γ’ _{i k}
(x’) ==> λ γ’ _{i k}
(λx). The Cosmod transformation ensures that the mass of a Spin 2 particle in a given space-time universe may be related to the mass of Spin 2 particle of another space-time universe. The graviton-like quanta would have extremely low mass of the order of 1E-103 g, with quantum number ξ_f =-1, and m _f = 1250 MeV: f being the symbol for f-meson. The formula suggested is m _g = m_f exp [-2 ξ_fΔ f].
It has been the suggestion of the author in the years 1976-1977 that based on the considerations of graviton-like quanta of Spin 2 and their inherent symmetry relation (or of its violation) with other Spin 2 particles of elementary particle physics classified under the unitary symmetry, gave an imputes to conjecture the possible existence of STRANGE STARS widely reported almost all the leading daily newspapers in India.
Realization of the strange stars in terms of the General Theory of Relativity of gravitation and Einstein like relativistic field equations has been a long standing desire of the present author. The present article is one of a culminating work to this desire.
STRANGENESS APPROACH TO DETERMINE OTHER PHYSICAL STRENGTHS:
The distinctive feature of the present calculation is the adoption of an asymmetric covariant connection coefficient to be the source of gravitational strangeness. Moreover it has been associated to occur with the G ² ₂. I prefer to present the details of the theory by way of graphical illustrations of the various physical entities. The Figs 1,2,3,4,5 respectively demonstrate the nature of the variations of the physical entities strength of the gravitational strangeness ‘gs’, square of the magnetic monopole strength ‘gm2’, the absolute of the electric field strength ‘e2’, the string quark energy density ‘ rs’ and the proper energy density ‘rh’. Please note that I have used a different notation in the graphical illustrations to signify the physical entities unlike the standard letters mentioned above.

CONCLUSIONS AND SUMMARY:
Present model clearly projects the determination of the role of cosmological magnetic field consistent with a number of astrophysical constraints and the geometric features of the possible new gravitational strangeness. The idea of primordial magnetism through a geometrical approach of strange field is a significant finding of the present work. Large-scale fields observed as seen in the universe today via the characteristics of the high-red shift proto-galaxies thus presumably has its origin in the gravitational strange field a result of the asymmetric covariant connection coefficients. To the present author’s knowledge no one has ever thought of gravitational strangeness. Thus, possibly if one sticks to the string cosmology model then strings need themselves to be gravitationally strange.

Acknowledgment:
The author is deeply indebted to late Professor K. Rangadhama Rao D.Sc. (Madras) D.Sc. (London) for inspiring research endeavour and sustained encouragement.

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ADDENDUM:

*thefts that have occurred in my residence(and as endorsed on 1st Dec 2009 by the concerned authority ) have greatly hampered my studies.