The non-axisymmetrical configuration of a large-scale solar and stellar magnetic field

The non-axisymmetric and nonlinear solutions of the magnetostatic equations are given in three-dimensional space of spherical coordinates (r, θ, ?). These solutions are applied to the large-scale solar magnetic field. Their basic features are similar to a dipole field near the polar regions and the polarity reverses near the equator. These features agree with observations for the large-scale solar magnetic field. The solutions can also be applied to investigating the connection between the structure of the magnetic field and the density distribution of the corona. It is shown that the tops of the closed magnetic field associate with density enhancements. Similar results may apply to the large-scale configuration of the stellar field.     

Solutions of Einstein-Maxwell field equations for a static charged perfect fluid shphere

The object of this paper is to give a new mathematical and physical method of finding explicit analytical interior solutions of the Einstein-Maxwell field equations of a static perfect fluid sphere with charge. In spite of many successful efforts in solving the field equations, the importance of finding meaningful general analytic solutions remains. Our purpose is to obtain the interior solutions of the field equations that they complete the results, which they have been already published in an earlier paper (Dionysiou, 1982; this paper will be referred to hereafter as Paper I). Using our new formulae, we then rederive some known results as particular solutions.     

Cosmological Massive Scalar Field Interacting with Viscous Fluid

Relativistic cosmological field equations are obtained for a Robertson-Walker space time interacting with viscous fluid and massive scalar field. The cosmological solutions to the field equations are obtained and the nature of the scalar field as well as the viscous fluid are studied. It is found that the solutions obtained are realistic only for a closed Universe. This revised version was published online in July 2006 with corrections to the Cover Date.     

Cylindrically symmetric cosmologies in Lyra geometry

A class of new exact solutions of the Einstein field equations have been investigated for stationary cylindrically symmetric space-time around a local cosmic string in the theory based on Lyra’s geometry in normal gauge in the presence and absence of an electromagnetic field. The cosmological solutions have been analyzed through various physical and geometrical parameters. It has also been shown that the solutions are space-time inhomogeneous and filled with charged dust.     

Non-linear tearing structures in equilibrium current sheet

A family of exact analytic solutions of the time-independent Vlasov-Maxwell equations is presented. The solutions describe two-dimensional equilibrium current sheet with magnetic field structures resembling that produced by the tearing instability. In particular, the solutions presented here do not restrict the field in the magnetic island to small magnitude. It is shown that as the scale length of the magnetic island increases, the thickness of the current sheet increases while the average current and the average magnetic energy decrease. The tearing structures described by the solutions may exist in the magnetotail current sheet, the magnetopause current layer and the field-aligned auroral sheet current.     

Massive scalar field interacting with viscous fluid distribution in cosmological models

The study of Einstein's field equations describing Robertson-Walker cosmological models with massive scalar field and viscous fluid representing the matter has been made. The problem has been investigated with and without the source density in the wave equation. Corresponding exact solutions of the field equations have been obtained under different physical equations of state: namely, (i) dust distribution, (ii) Zeldovich fluid distribution, (iii) disordered distribution of radiation subject to physically realistic conditions. The physical interpretations of the physically realistic solutions has been investigated. It has been found that physically realistic solutions has been obtained for closed cosmological models only.     

Relativistic models of magnetars: the twisted torus magnetic field configuration

We find general relativistic solutions of equilibrium magnetic field configurations in magnetars, extending previous results of Colaiuda et al. Our method is based on the solution of the relativistic Grad–Shafranov equation, to which Maxwell's equations can be reduced. We obtain equilibrium solutions with the toroidal magnetic field component confined into a finite region inside the star, and the poloidal component extending to the exterior. These so-called twisted torus configurations have been found to be the final outcome of dynamical simulations in the framework of Newtonian gravity, and appear to be more stable than other configurations. The solutions include higher-order multipoles, which are coupled to the dominant dipolar field. We use arguments of minimal energy to constrain the ratio of the toroidal to the poloidal field.     

Maximum mass of magnetic white dwarfs

We revisit the problem of the maximum masses of magnetized white dwarfs(WDs).The impact of a strong magnetic field on the structure equations is addressed.The pressures become anisotropic due to the presence of the magnetic field and split into parallel and perpendicular components.We first construct stable solutions of the Tolman-Oppenheimer-Volkoff equations for parallel pressures and find that physical solutions vanish for the perpendicular pressure when B(?) 10~(13) G.This fact establishes an upper bound for a magnetic field and the stability of the configurations in the(quasi) spherical approximation.Our findings also indicate that it is not possible to obtain stable magnetized WDs with super-Chandrasekhar masses because the values of the magnetic field needed for them are higher than this bound.To proceed into the anisotropic regime,we can apply results for structure equations appropriate for a cylindrical metric with anisotropic pressures that were derived in our previous work.From the solutions of the structure equations in cylindrical symmetry we have confirmed the same bound for B ~ 10~(13) G,since beyond this value no physical solutions are possible.Our tentative conclusion is that massive WDs with masses well beyond the Chandrasekhar limit do not constitute stable solutions and should not exist.     

Exact Brans-Dicke bianchi type-I vacuum solutions with a cosmological constant

Exact cosmological solutions of the vacuum Brans-Dicke field equations are derived. The solutions are the anisotropic generalizations of the isotropic de Sitter solutions of the general theory of relativity.     

The general class of Bianchi cosmological models with viscous fluid and particle creation in Brans-Dicke theory

This paper deals with the general class of Bianchi cosmological models with bulk viscosity and particle creation described by full causal thermodynamics in Brans-Dicke theory. We discuss three types of average scale-factor solutions for the general class of Bianchi cosmological models by using a special law for the deceler- ation parameter which is linear in time with a negative slope. The exact solutions to the corresponding field equations are obtained in quadrature form and solutions to the Einstein field equations are obtained for three different physically viable cosmologies. All the physical parameters are calculated and discussed in each model.     

Effects of Magnetic Field and Opacity on Self-Similar YSO Flow Models

During star formation, both infall and outflows are present around protostellar cores. Here we show solutions of a self-similar model that study the two flows with only one set of equations. We focus here on the effects of magnetic field and dust on solutions. Unmagnetized solutions have also been found. This shows that magnetic field is not the main driving mechanism of the circulation process. We have found that a reduction of magnetic field produces denser, slower and narrower outflows. When the opacity is less dominated by dust, density increases in the equatorial region, allowing larger accretion rates to occur. The comprehension of massive star formation could be related to this latter effect.     

Anisotropic spheres with uniform energy density in bimetric theory of relativity

In this paper we have obtained interior solutions of the field equations for anisotropic sphere in the bimetric general relativity theory formulated by Rosen (Lett. Nuovo Cimento 25, 1979). A class of solutions for a uniform energy-density source of the field equations is presented. The analytic solutions obtained are physically reasonable, well behaved in the interior of the sphere. The solutions agree with the Einstein’s general relativity for a physical system compared to the size of the universe such as the solar system.     

A collective radiation mechanism for the core emission of pulsars

A study of imperfect fluid interacting with the gravitational field for spherically-symmetric Robertson-Walker metric has been carried out. Exact solutions of the field equations of viscous fluid have been obtained under different equations of state. The corresponding physical interpretations of the solutions have been investigated. It has been shown that the occurrence of Big-Bang does not take place when the viscous fluid as only source term interacts with the gravitational field at the initial stages.     

Cosmological scalar fields that mimic the ΛCDM cosmological model

We look for cosmologies with a scalar field (dark energy without cosmological constant), which mimic the standard ΛCDM cosmological model yielding exactly the same large-scale geometry described by the evolution of the Hubble parameter (i.e. photometric distance and angular diameter distance as functions on z). Asymptotic behavior of the field solutions is studied in the case of spatially flat Universe with pressureless matter and separable scalar field Lagrangians; the cases of power-law kinetic term and power-law potential are considered. Exact analytic solutions are found in some special cases. A number of models have the field solutions with infinite behavior in the past or even singular behavior at finite redshifts. We point out that introduction of the cosmological scalar field involves some degeneracy leading to lower precision in determination of Ω _m . To remove this degeneracy additional information is needed besides the data on large-scale geometry. The article is published in the original.     

String cosmological models of Bianchi type-III

A technique to generate new exact Bianchi type-III cosmological solutions of massive strings in the presence of magnetic field is presented. Starting from Tikekar and Patel's strings models in the absence and presence of the magnetic field, new solutions are obtained. Some of their physical features are discussed.     

Exact Brans-Dicke-Bianchi types-II,VIII, and IX stiff matter solutions

Exact solutions of the Brans-Dicke field equations of Bianchi types-II, VIII, and IX are derived. The solutions represent locally rotationally symmetric universes with stiff matter content.     

Spherical radiation-driven shock waves in a non-uniform atmosphere

Similarity solutions are obtained for spherical radiation-driven shock waves propagating in a non-uniform atmosphere at rest obeying a density power law. Approximate analytical solutions are also obtained and found to be in good agreement with the numerical solutions. The effect of the parameter characterizing the initial density distribution of the gas on solutions of the flow field is studied in detail. It is also shown analytically that the shock wave propagates as an overdriven detonation.     

The plane symmetric vacuum solutions of modified field equations in metric f(R) gravity

The f(R) theories of gravity have been interested in recent years. A considerable amount of work has been devoted to the study of modified field equations with the assumption of constant Ricci scalar which may be zero or nonzero. In this paper, the exact vacuum solutions of plane symmetric spacetime are analyzed in f(R) theory of gravity. The modified field equations are studied not only for R=constant but also for general case R≠constant. In particular, we show that the Novotný-Horský and anti-de Sitter spacetimes are the exact solutions of the field equations with the non-zero constant Ricci scalar. Finally, the family of solutions with R≠constant is obtained explicitly which includes the Novotný-Horský, Kottler-Whittaker, Taub and conformally flat spacetimes.     

Notes on applications of general relativity in free space : implication from the motion of a test particle

The equations of motion of a neutral test particle in the field obtained by Wanas (1990) are completely solved. The solution obtained is compared with corresponding solutions in the cases of the Reissner-Nordstrom field, the Kerr field, and the Kerr-Newman field. The comparison shows that the new constant, appeared in the field considered, is connected to electromagnetism and not to spin phenomena.