An inhomogeneous stiff fluid universe with electromagnetic field in general relativity

An inhomogeneous cylindrically symmetric cosmological model for stiff perfect fluid distribution with electromagnetic field is obtained.F ₁₂ is the non-vanishing component of electromagnetic field tensor. The metric potentials are functions ofx andt both. The behaviour of the electromagnetic field tensor together with geometrical and physical aspects of the model are also examined.     

Inhomogeneous perfect fluid universe with electromagnetic field

Cylindrically symmetric inhomogeneous cosmological model for perfect fluid distribution with electromagnetic field is obtained. The source of the magnetic field is due to an electric current produced along the z-axis. F ₁₂ is the non-vanishing component of electromagnetic field tensor. To get the deterministic solution, it has been assumed that the expansion θ in the model is proportional to the shear σ. Physical and geometric aspects of the models are also discussed in presence and absence of magnetic field.      

The Einstein-Maxwell field equations,II

In order to arrive at more general results solving Einstein-Maxwell's equations our investigation is centered around an electromagnetic spin tensor, which must be chosen in such a way that conservation laws still hold. This notion of the combined tensor is of course closely linked with the unified field equations. We shall avoid in this way the problem of the form of the matter tensor and neglect non-linear gravitational terms in the Ricci tensor. Then, the field equations have as solutionsh _ij=h _ij ^(P) +h _ij ^(h) , whereh _ij ^(P) are particular solutions, which are obtained by direct calculations andh _ij ^(h) are solutions of h _ij ^(h) =0. The quantitiesh _ij ^(P) are purely electromagnetic in nature, whileh _ij ^(h) may represent purely gravitational terms. The results obtained complete the ones which have been published already in the preceeding paper (Dionysiou, 1980a; which will hereafter be referred to as Paper I).     

Cylindrically symmetric inhomogeneous universe with electromagnetic field in string cosmology

Cylindrically symmetric inhomogeneous string cosmological model in presence of electromagnetic field is investigated. We have assumed that F ₂₃ is the only non-vanishing component of F _ij . To get the deterministic solution, it has been assumed that the expansion (θ) in the model is proportional to the eigen value σ ¹ ₁ of the shear tensor σ ⁱ _j . The physical and geometric aspects of the model are also discussed.      

Magnetized string cosmological model in cylindrically symmetric inhomogeneous universe-revisited

Cylindrically symmetric inhomogeneous magnetized string cosmological model is investigated. The source of the magnetic field is due to an electric current produced along x-axis. F ₂₃ is the only non-vanishing component of electromagnetic field tensor. To get the deterministic solution, it has been assumed that the expansion (θ) in the model is proportional to the eigen value σ ₁ ¹ of the shear tensor σ _j ⁱ . The physical and geometric properties of the model are also discussed in presence and absence of magnetic field.     

Plane symmetric inhomogeneous perfect fluid universe with electromagnetic field in Lyra geometry

A new class of plane-symmetric inhomogeneous cosmological models of perfect fluid distribution with electro-magnetic field based on Lyra’s geometry is obtained by considering a time dependent displacement field. The source of the magnetic field is due to an electric current produced along the z-axis. Only F ₁₂ is a non-vanishing component of electromagnetic field tensor. To get the deterministic solutions, the free gravitational field is assumed to be of Petrov type-II non-degenerate. It has been found that the displacement vector β(t) behaves like cosmological term Λ which is consistent with the recent observations of type Ia supernovae. It is also observed that β(t) affects entropy. Some geometric and physical behaviour of the models are also discussed in presence of magnetic field.      

Dynamics of a magnetized Bianchi VI 0 universe with anisotropic fluid

We discuss spatially homogeneous and anisotropic Bianchi type VI ₀ cosmological model with anisotropic fluid and magnetic field. The energy-momentum tensor consists of anisotropic fluid with anisotropic EoS and a uniform magnetic field of energy density ρ _B . Exact solution of the field equations is obtained by using the condition that expansion is proportional to the shear scalar. We focus on the future evolution of the model both in the presence and absence of magnetic field. In particular, we address the question whether these models approach to isotropy.     

Dynamics of Kantowski-Sachs universe with magnetized anisotropic Dark Energy

Kantowski-Sachs cosmological model in the presence of magnetized anisotropic dark energy is investigated. The energy-momentum tensor consists of anisotropic fluid with anisotropic EoS p=ωρ and a uniform magnetic field of energy density ρ _B . We obtain exact solutions to the field equations using the condition that expansion is proportional to the shear scalar. The physical behavior of the model is discussed with and without magnetic field. We conclude that universe model as well as anisotropic fluid does not approach isotropy through the evolution of the universe.     

Unrestricted second-order tensor virial equations for linear oscillations of magnetic configurations

This paper deals with the second-order tensor virial equations for the linear oscillations of a gaseous mass in the presence of a magnetic field. It is shown that the commonly used linearized versions of the tensor virial equations are restricted integral equations that incorporate the linearized equation of motion but not the boundary condition. These restricted equations only allow trial functions that fulfil the boundary condition and are of limited practical value.The unrestricted variational principle for the linear oscillations of a magnetic configuration is used to derive a more general formulation of the second-order tensor virial equations so that the linear trial function _i =X _ij x _j can be used to study the oscillations of a configuration with a magnetic field that extends in the exterior vacuum. The unrestricted virial equations have been applied to Ferraro's model and approximate results for the eigenfrequencies and eigenfunctions have been obtained for nine oscillation modes.     

Generation of a d.c. field by nonlinear electromagnetic waves in relativistic plasmas

A finite amplitude linearly polarized electromagnetic wave propagating in a relativistic plasma, is found to generate the longitudinal d.c. as well as the oscillating electric field at the second harmonic. In a plasma consisting of only electrons and positrons, these fields cannot be generated.The evolution of the electromagnetic waves is governed by the non-linear Schrödinger equation which shows that the electromagnetic solitons are always possible in ultra-relativistic plasmas (electron-ion or electron-positron) but in a plasma with relativistic electrons and nonrelativistic ions, these solitons exist only if 1(KT _e/m_eC²)<(2m _i/15m_e);m _e andm _i being the electron and ion mass andT _e the electron temperature. Both the d.c. electric field and the solitons provide a nonlinear mechanism for anomalous acceleration of the particles. This model has direct relevance to some plasma processes occurring in pulsars.     

The conformal potential of the stationary axisymmetric vacuum

In a stationary axisymmetric vacuum gravitational field, the conformal structure of the 3-space is determined by the symmetric, trace free and divergence-less tensor Y_ir. Using the Killing vector Kⁱ of the axisymmetry, the conformal potential U can be defined by U,_i = _εijkKjY^krK_r. Conversely, the tensor Y_ik is given algebraically in terms of the gradient U,_i of the conformal potential. An attempt is made here to re-formulate the field equations R_λμ = 0 in terms of the conformal potential. Introducing the Ernst potential as a complex coordinate, the cylindrical radius can be eliminated from the field equations.     

Compactification and cosmic string phenomenology

A U(1) model of gravitational, Higgs and, gauge fields is analysed. Two phases of the system are considered. In the case with broken symmetry we have the Nielsen-Olesen configuration. In the symmetric phase we find a space-time metric S² × E₁². This appears in full analogy to the Freund-Rubin compactification due to an antisymmeric tensor field. The connection of these structures with cosmic string phenomenology is analysed.     

Cosmological Models with ‘Some’ Variable Constants

Various models are considered with metric type flat FRW i.e. with k = 0 whose energy-momentum tensor is described by a perfect fluid whose generic equation of state is p = ωρ and taking into account the conservation principle div(T _i ^j ) = 0, but considering some of the‘constants’ as variable. A set of solutions through dimensional analysis is trivially found. The numeric calculations carried out show that the results obtained are not discordant with those presently observed for cosmological parameters together with the electromagnetic and quantum quantities. This revised version was published online in July 2006 with corrections to the Cover Date.     

The Influence of a Uniform Magnetic Field of Arbitrary Strength on Turbulence

The spectral tensor of turbulent motion in an infinite conductive incompressible medium is given in the case of a uniform magnetic field of any strenght affecting a homogeneous turbulence. With the help of BOCHNER 's theorem we make sure that the trace u_i(x, t) u_i(x, t) is non-negative. The presence of a weak magnetic field causes a damping of the turbulence, in some cases a strengthening. For strong magnetic fields the norms of the velocity vectors parallel and perpendicular to B approach one and the same value. Compared with the correlation length measured perpendicular to the magnetic field the correlation length measured along the magnetic field increases. Furthermore, our formulas have allowed to calculate the dependence of the α-effect on the magnetic field.     

Bianchi Type I Magnetized String Cosmological Model in General Relativity

Bianchi Type I magnetized string cosmological model following the techniques used by Letelier and Stachel, is investigated. To get a determinate model, we assume a condition ∊ = λ (geometric string) where ∊ is the rest energy density, λ the string tension density and expansion (θ) is proportional to eigen value σ₁ ¹ of shear tensor (σ _j ⁱ ), which leads to A = ℓ (BC) ⁿ where A, B, C are metric potentials and ℓ and n are constants. The behaviour of the model in presence and absence of magnetic field is discussed. The physical and geometrical aspects of the model are also discussed.     

The symmetric tensor field in the relativistic theory of gravitation

The system of a self-gravitating scalar field is frequently used in inflationary cosmological models. In the present paper we study a more complicated system containing an extra linear tensor field _ik=_ki with minimal coupling. We determine five of the six free parameters that occur in the most general expression for the actionS of this field. In doing so we assume that in flat space-time the field _ik must be invariant under gauge transformations. In a special case theS found becomes a known expression for the action of a massless tensor field _ik. We compute the metric energy-momentum tensor that determines the contribution of _ik to the Einstein equations. We also exhibit the equations of motion of _ik in curved space-time.Translated fromAstrofizika, Vol. 38, No. 3, 1995.     

Exact solution of perfect fluid massive string cosmology in Bianchi type?III space-time with 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 20:2414, 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. The vacuum energy density Λ is found to be positive and a decreasing function of time which is supported by the results from recent supernovae Ia observations. It is also observed that in early stage of the evolution of the universe string dominates over the particle whereas the universe is dominated by massive string at the late time. Some physical and geometric properties of the model are also discussed.     

Singular points of the polarization tensor

The problem to compute the magnetic field above the chromosphere using data of the vector = B _t/Bt that gives the projected field direction can be solved with different approximations. The field of direction vectors is, however, not the only field accessible to observations. The Stokes parameters, which are components of the radiation tensor, can be measured at each point of the image plane. The directions of the eigenvectors of the radiation tensor define two mutually orthogonal systems of integral curves in the image plane. These families of curves have singular points, which are generally of different type than those of the vector field. When the morphology of H chromospheric fibrils are used to infer the topology of the magnetic field, a similar problem is met, suggesting that singular points should also be present there.     

Some magnetized bulk viscous string cosmological models in?General Relativity

Some Bianchi type-I viscous fluid string cosmological models with magnetic field are investigated. The viscosity coefficient of bulk viscous fluid is assumed to be a power function of mass density ξ(t)=ξ ₀ ρ ^m , where ξ ₀ and m are constants. To get a determinate model, we assume conditions ρ=(1+ω)λ, where ρ is rest energy density, ω a positive constant and λ the string tension density and expansion θ is proportional to eigen value σ ₁¹ of the shear tensor σ _j ⁱ . The behaviour of the models from physical and geometrical aspects in presence and absence of magnetic field is discussed.      

Jovian magnetospheric ion cyclotron instability in the presence of parallel electric field

A dispersion relation for left hand circularly polarized electromagnetic wave propagation in an anisotropic magnetoplasma in the presence of a very weak parallel electrostatic field has been derived with the help of linearized Vlasov and Maxwell equations. An expression of the growth rate has been derived in presence of parallel electric field for ion-cyclotron electromagnetic wave in an anisotropic media. The modification made in the growth rate by introducing parallel electric field and temperature anisotropy has been studied for fully ionized hydrogen plasma with the help of observations made on Jovian ionosphere and magnetosphere atL = 5.6 R_j. It is concluded that the growth (damping) of ion-cyclotron electromagnetic wave is possible when the wave vector is parallel (antiparallel) to the static electric field and effect is more pronounced at higher wave number.