Five Dimensional Axially Symmetric String Cosmological Models with Bulk Viscous Fluid

Bulk viscous fluid distribution with massive strings in LRS Bianchi type-1 space time is studied. The exact solutions of the field equations are obtained by using the equation of state ρ=−λ and ρ=λ. We observed that the bulk viscous fluid does not survive for ρ=−λ whereas it survives for ρ=λ. Some physical and geometrical properties of the models are discussed.     

Anisotropic Bianchi Type-I String Cosmological Models in Normal Gauge for Lyra’s Manifold with Constant Deceleration Parameter

The present study deals with a spatially homogeneous and anisotropic Bianchi type-I (B-I) cosmological models representing massive strings in normal gauge for Lyra’s manifold by applying the variation law for generalized Hubble’s parameter that yields a constant value of deceleration parameter. The variation law for Hubble’s parameter generates two types of solutions for the average scale factor, one is of power-law type and other is of the exponential-law type. Using these two forms, Einstein’s modified field equations are solved separately that correspond to expanding singular and non-singular models of the universe respectively. The energy-momentum tensor for such string as formulated by Letelier, P.S.: Phys. Rev. D 28, 2414 (1983) is used to construct massive string cosmological models for which we assume that the expansion (θ) in the model is proportional to the component s¹ ₁\sigma^{1}_{~1} of the shear tensor s^j _i\sigma^{j}_{~i}. This condition leads to A=(BC) ^m , where A, B and C are the metric coefficients and m is proportionality constant. Our models are in accelerating phase which is consistent to the recent observations. It has been found that the displacement vector β behaves like cosmological term Λ in the normal gauge treatment and the solutions are consistent with recent observations of SNe Ia. It has been found that massive strings dominate in the both decelerating and accelerating universes. The strings dominate in the early universe and eventually disappear from the universe for sufficiently large times. This is in consistent with the current observations. Some physical and geometric behaviour of these models are also discussed.     

String cosmology in LRS Bianchi type-II dusty Universe with time-decaying vacuum energy density Λ

A model of a cloud formed by massive strings is used as a source of LRS Bianchi type-II with time-decaying vacuum energy density Λ. To construct string cosmological models, we have used the energy–momentum tensor for such strings as formulated by Letelier (1983). The high nonlinear field equations have been solved for two types of strings: (i) massive string and (ii) Nambu string. The expansion θ in the model is assumed to be proportional to the shear σ. This condition leads to A = βB ^m , where A and B are the metric coefficients, m is a constant and β is an integrating constant. Our models are in accelerating phase which is consistent with the recent observations of supernovae type-Ia. The physical and geometrical behaviour of these models are also discussed.     

Lyra’s Cosmology of Massive Strings in Anisotropic Bianchi-II Space-Time

The paper deals with a spatially homogeneous and totally anisotropic Bianchi II cosmological models representing massive strings in normal gauge for Lyra’s manifold. The modified Einstein’s field equations have been solved by applying variation law for Hubble’s parameter. This law generates two type of solutions for average scale factor, one is of power law type and other is of exponential law type. The power law describes the dynamics of Universe from big bang to present epoch while exponential law seems reasonable to project dynamics of future Universe. It has been found that the displacement vector (β) is a decreasing function of time and it approaches to small positive value at late time, which is collaborated with Halford (Aust. J. Phys. 23, 863, 1970) as well as recent observations of SN Ia. The study reveals that massive strings dominate in early Universe and eventually disappear from Universe for sufficiently large time, which is in agreement with the current astronomical observations.     

Bianchi Type <Emphasis Type="Italic">VI</Emphasis><Subscript>0</Subscript> Magnetized Barotropic Bulk Viscous Fluid Massive String Universe in General Relativity

A model of a cloud formed by massive strings is studied in the context of the usual general relativity. This model is used as a source of Bianchi type VI ₀ massive with magnetic field and bulk viscosity. To get a determinate model, we assume that the expansion (θ) in the model is proportional to the shear (σ) and also the fluid obeys the barotropic equation of state. The behaviour of the models from physical and geometrical aspects in presence and absence of magnetic field and bulk viscosity is discussed.     

Magnetized Bianchi Type III String Universe with Time Decaying Vacuum Energy Density Λ

Exact solution of Einstein’s field equations is obtained for massive string cosmological model of Bianchi III space-time using the technique given by Letelier (Phys. Rev. D 28:2414, 1983) in presence of perfect fluid and decaying vacuum energy density Λ. To get the deterministic solution of the field equations the expansion θ in the model is considered as proportional to the eigen value s² ₂\sigma^{2}_{~2} of the shear tensor s^j _i\sigma^{j}_{~i} and also the fluid obeys the barotropic equation of state. It is observed that the particle density and the tension density of the string are comparable at the two ends and they fall off asymptotically at similar rate. But in early stage as well as at the late time of the evolution of the universe we have two types of scenario (i) universe is dominated by massive strings and (ii) universe is dominated by strings depending on the nature of the two constants L and ℓ. The value of cosmological constant Λ for the model is found to be small and positive which is supported by the results from recent supernovae Ia observations. Some physical and geometric properties of the model are also discussed.     

Global strings in extra dimensions: The full map of solutions,matter trapping,and the hierarchy problem

We consider (d ₀ + 2)-dimensional configurations with global strings in two extra dimensions and a flat metric in d ₀ dimensions, endowed with a warp factor e ^2γ depending on the distance l from the string center. All possible regular solutions of the field equations are classified by the behavior of the warp factor and the extradimensional circular radius r(l). Solutions with r → ∞ and r → const > 0 as l → ∞ are interpreted in terms of thick brane-world models. Solutions with r → 0 as l → l _c > 0, i.e., those with a second center, are interpreted as either multibrane systems (which are appropriate for large enough distances l _c between the centers) or as Kaluza-Klein-type configurations with extra dimensions invisible due to their smallness. In the case of the Mexican-hat symmetry-breaking potential, we build the full map of regular solutions on the (ɛ, Γ) parameter plane, where ɛ acts as an effective cosmological constant and Γ characterizes the gravitational field strength. The trapping properties of candidate brane worlds for test scalar fields are discussed. Good trapping properties for massive fields are found for models with increasing warp factors. Kaluza-Klein-type models are shown to have nontrivial warp factor behaviors, leading to matter particle mass spectra that seem promising from the standpoint of hierarchy problems. The text was submitted by the authors in English.     

Anisotropic Bianchi Type-II Massive String Cosmological Models with Time-Decaying Λ Term and Thermodynamic Parameters

The present paper envisages a spatially homogeneous and anisotropic Bianchi II massive string cosmological models with time-decaying Λ term in general relativity. By using the variation law of Hubble’s parameter, the Einstein’s field equations have been solved for two general cases. The first case involving a power law solution describes the dynamics of universe from big bang to present epoch while the second case admit an exponential solution seems reasonable to project dynamics of future universe. We observed that massive strings dominate in early universe and eventually disappear at late time, which is consistent with the current astronomical observations. It has been found that the cosmological constant (Λ) is a decreasing function of time and it approaches to small positive value at sufficiently large time. The thermodynamic properties of anisotropic Bianchi II universe are studied and also the absolute temperature and entropy distribution are given explicitly. The relations between thermodynamic parameters and cosmological constant Λ has been established. Physical behavior of the derived model is elaborated in detail.     

Static models of cosmic strings in general relativity

Exact solutions to Einstein’s equations for a cloud of massive strings with a general static metric representing spherical plane and hyperbolic symmetries are derived. Some properties of massive strings for different cases are also discussed.     

Bianchi Type-III Cosmic Strings and Domain Walls Cosmological Model in General Relativity

Bianchi type-III space time is considered in the presence of cosmic strings and thick domain walls source in the frame work of general relativity. Exact cosmological models using various cases of ρ=α λ and p=γ ρ are presented. It is observed that the behavior of these models (with cosmic strings and domain walls), based on their physical and kinematical properties, is found to be identical.     

String Cosmological Solutions in Self-Creation Theory of Gravitation

We have studied the problem of cosmic strings for Bianchi-I, II, VIII and IX string cosmological models in Barber’s (Gen. Relativ. Gravit. 14:117, 1982) second self—creation theory of gravitation. We have obtained some classes of solutions by considering different functional form for metric potentials. It is also observed that due to the presence of scalar field, the power index ‘m’ of the metric coefficients has a range of values.     

Magnetized String Cosmology in Anisotropic Bianchi-II Space-time with Variable Cosmological Term-Λ

The present study deals with a spatially homogeneous and anisotropic Bianchi-II cosmological models representing massive strings by applying the variation law for generalized Hubble’s parameter that yields a constant value of deceleration parameter. We find that the constant value of deceleration parameter is reasonable for the present day universe. The variation law for Hubble’s parameter generates two types of solutions for the average scale factor, one is of power-law type and other is of the exponential form. Using these two forms, Einstein’s field equations are solved separately that correspond to expanding singular and non-singular models of the universe respectively. The energy-momentum tensor for such string as formulated by Letelier (Phys. Rev. D 28:2414, 1983) is used to construct massive string cosmological models for which we assume that the expansion (θ) in the model is proportional to the component s¹₁\sigma^{1}_{1} of the shear tensor s^j_i\sigma^{j}_{i}. This condition leads to A=(BC) ^m , where A, B and C are the metric coefficients and m is proportionality constant. Our models are in accelerating phase which is consistent to the recent observations. The cosmological constant Λ is found to be a decreasing function of time and it approaches a small positive value at present epoch which is in good agreement by the results from recent supernovae observations. Some physical and geometric behaviour of the models are also discussed.     

Hawking Radiation of Charged Particles from a Rotating Black String

Using Damour-Ruffini method, Hawking radiation of rotating black strings is studied. Under the condition that the total energy, total angular momentum and total charge are conservative, the transition probability from initial state (energy M+ω, charge Q+e and angular momentum J+m) to final state (energy M, charge Q and angular momentum J) for black strings is derived considering the reaction of radiation particles to spacetime. That is, the probability that black strings radiate particles with energy ω, charge e and angular momentum m is obtained. The real spectrum is not a strictly pure thermal spectrum. Our result is consistent with Parikh and Wilczek’s result. It satisfies the unitary principle of quantum mechanics. However, in our result there are not only the term that denotes effect of energy and charge of radiation particles but also the term that denotes effect of radiation particles angular momentum on rotating black strings angular momentum. We provide a new way for investigating radiation of black strings.     

Nonequilibrium parton dynamics in the strongly interacting QGP

The dynamics of partons, hadrons and strings in relativistic nucleus-nucleus collisions is analyzed within the novel Parton-Hadron-String Dynamics (PHSD) transport approach, which is based on a dynamical quasiparticle model for partons (DQPM) matched to reproduce recent lattice-QCD results—including the partonic equation of state—in thermodynamic equilibrium. The transition from partonic to hadronic degrees of freedom is described by covariant transition rates for the fusion of quark-antiquark pairs or three quarks (antiquarks), respectively, obeying flavor current-conservation, color neutrality as well as energymomentum conservation. Since the dynamical quarks and antiquarks become very massive close to the phase transition, the formed resonant ‘pre-hadronic’ color-dipole states (q [`(q)]\bar q or qqq) are of high invariant mass, too, and sequentially decay to the groundstate meson and baryon octets increasing the total entropy. When applying the PHSD approach to Pb + Pb colllisions at 158 A GeV we find a significant effect of the partonic phase on the production of multi-strange antibaryons due to a slightly enhanced s [`(q)]\bar q pair production from massive time-like gluon decay and a larger formation of antibaryons in the hadronization process.     

Quasi-Stationary States for Particle Systems in the Mean-Field Limit

We prove that the N particles approximation of a class of stable stationary solutions of the Vlasov equation is uniformly valid on a time scale N ^β for β>0 (explicitly given in various cases) much longer than the usual log N scale. The vortex blob method in dimension 2 is also discussed. The result applies to a class of stationary solutions more general than in a previous work.     

Black holes under external influence

The work on black holes immersed in external fields is reviewed in both test-field approximation and within exact solutions. In particular we pay attention to the effect of the expulsion of the flux of external fields across charged and rotating black holes which are approaching extremal states. Recently this effect has been shown to occur for black hole solutions in string theory. We also discuss black holes surrounded by rings and disks and rotating black holes accelerated by strings. The content corresponds to the lecture given at ICGC 2000 in Kharagpur. Sections 2–6 are based on the text of the lecture on ‘Electromagnetic fields around black holes and Meissner effect’ given at the 3rd ICRA workshop in Pescara 1999 (to be published with T Ledvinka in Nuovo Cimento).     

Brownian rotation of classical spins: dynamical equations for non-bilinear spin-environment couplings

Given two strings X and Y of N and M characters respectively, the Longest Common Subsequence (LCS) Problem asks for the longest sequence of (non-contiguous) matches between X and Y. Using extensive Monte-Carlo simulations for this problem, we find a finite size scaling law of the form for the average LCS length of two random strings of size N over S letters. We provide precise estimates of for .We consider also a related Bernoulli Matching model where the different entries of an array are occupied with a match independently with probability 1/S. On the basis of a cavity-like analysis we find that the length of a longest sequence of matches in that case behaves as where r=M/N and . This formula agrees very well with our numerical computations. It provides a very good approximation for the Random String model, the approximation getting more accurate as S increases. The question of the “universality class” of the LCS problem is also considered. Our results for the Bernoulli Matching model show very good agreement with the scaling predictions of [#!HwaLassig96_PRL!#] for Needleman-Wunsch sequence alignment. We find however that the variance of the LCS length has a scaling different from Var in the Random String model, suggesting that long-ranged correlations among the matches are relevant in this model. We finally study the “ground state” properties of this problem. We find that the number of solutions typically grows exponentially with N. In other words, this system does not satisfy “Nernst's principle”. This is also reflected at the level of the overlap between two LCSs chosen at random, which is found to be self averaging and to approach a definite value q _S <1 as . Received: 23 April 1998 / Revised: 30 July 1998 / Accepted: 14 August 1998     

A Perspective on Regularization and Curvature

A global connection on the Connes Marcolli renormalization bundle relates β-functions of a class of regularization schemes by gauge transformations, as well as local solutions to β-functions over curved space–time.     

Behavior as t → ∞ of solutions of a problem in mathematical physics

A class of solutions, decaying as t → ∞, of a two-dimensional model problem on the oscillations of an ideal rotating fluid in some domains with angular points is constructed explicitly. The existence of solutions whose L ₂-norms decrease more rapidly than any negative power of t is established.