Bianchi II,VIII, and IX viscous fluid cosmology

In this paper we study the exact solutions for a viscous fluid distribution in Bianchi II, VIII, and IX models. The metric is simplified by assuming a relationship between the coefficients of the metric tensor. Solutions are obtained in two special cases: in one an additional assumption is made where the matter density and the expansion scalar have a definite relation and in the other a barotropic equation of state of the formp= is assumed. While the Bianchi II solutions are already found in the literature the other two classes of solutions are apparently new.     

Modified Chaplygin gas and solvable F-essence cosmologies

The Modified Chaplygin Gas (MCG) model belongs to the class of a unified models of dark energy and dark matter. In this paper, we have modeled MCG in the framework of f-essence cosmology. By constructing an equation connecting the MCG and the f-essence, we solve it to obtain explicitly the pressure and energy density of MCG. As special cases, we obtain both positive and negative pressure solutions for suitable choices of free parameters. We also calculate the state parameter which describes the phantom crossing.     

Cosmic strings and viscous matter in a Kantowski-Sachs universe

We study the dynamics of a universe where the matter content is represented by a radially directed distribution of cosmic strings plus matter admitting both shear and bulk viscosity. We assume specific forms for the equation of state of both the strings and matter and discuss the cosmological solutions obtained.     

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.     

Compact models with regular charge distributions

We model a compact relativistic body with anisotropic pressures in the presence of an electric field. The equation of state is barotropic, with a linear relationship between the radial pressure and the energy density. Simple exact models of the Einstein–Maxwell equations are generated. A graphical analysis indicates that the matter and electromagnetic variables are well behaved. In particular, the proper charge density is regular for certain parameter values at the stellar center unlike earlier anisotropic models in the presence of charge. We show that the electric field affects the mass of stellar objects and the observed mass for a particular binary pulsar is regained. Our models contain previous results of anisotropic charged matter with a linear equation of state for special parameter values.     

Analytical solutions for the Newtonian gravitational field induced by matter within axisymmetric boundaries

An analytical method originally applied to the problem of the actuator disc in fluid mechanics has been applied to the closely analogous problem of constructing the classical Newtonian potential and attractions. The method can treat axisymmetric problems and also non-axisymmetric cases where matter is confined within axisymmetric boundaries. The potential and attractions for the generalized thin finite disc can be given in closed form in terms of elliptic integrals and elementary functions. For the general case of matter within an axisymmetric boundary, the potentials and attractions can be evaluated as one-dimensional integrals of albeit complex analytical expressions. These expressions represent the fields induced by matter in an extended region as a distribution of gravitating discs. For certain special cases, such as matter bounded by a circular cylinder and also for matter distributed in a spherical region, closed-form solutions can be given that appear to be new. Some non-axisymmetric results are also given for the thin disc of infinite radial extent.     

The Fragmentation of Asteroids – A Synopsis of Analytical Methods (Mitteilungen der Universitäts-Sternwarte Jena Nr. 119)

Basing on the author's work a review of the possibilities as well as the limits of treating the problem of the collisional history of the asteroids by analytical methods is given. Using empirical data on rock fragmentation and general principles like symmetry and mass conservation the distribution function of the fragments arising from a single collision is analytically formulated. The size distribution of asteroids adjusting when crushing collisions have taken place a sufficiently long time can be obtained as the solution of an integrodifferential equation with partial derivatives (equation of fragmentation). Quasi-stationary solutions of the equation of fragmentation are discussed for particular cases. The problem of the steady state is reduced to the solution of a transcendental equation. The results obtained show that analytical methods already offer a good theoretical understanding of the observed size distribution of the asteroids. They should be, therefore, a useful basis of carrying out numerical calculations.     

Could pressureless dark matter have pressure?

A two-fluid dark matter model, in which dark matter is represented as a two-component fluid thermodynamic system, without interaction between the constituent particles of different species, and with each distinct component having a different four-velocity, was recently proposed in Harko and Lobo [T. Harko, F.S.N. Lobo, Phys. Rev. D 83 (2011) 124051]. In the present paper we further investigate the two-fluid dark matter model, by assuming that the two dark matter components are pressureless, non-comoving fluids. For this particular choice of equations of state the dark matter distribution can be described as a single anisotropic fluid, with vanishing tangential pressure, and non-zero radial pressure. We investigate the properties of this model in the region of constant velocity galactic rotation curves, where the dynamics of the test particles is essentially determined by the dark matter only. By solving the general relativistic equations of mass continuity and hydrostatic equilibrium we obtain the geometric and physical parameters of the dark matter halos in the constant velocity region in an exact analytical form. The general, radial coordinate dependent, functional relationship between the energy density and the radial pressure is also determined, and it differs from a simple barotropic equation of state.     

The equation of polarization transfer in an inhomogeneous magnetized plasma

Following the formalism on the polarization transfer equation presented recently by the same authors, solutions to this transfer equation under several special cases of interest are discussed in this paper. Analytic solutions for the Stokes parameters for several special cases of interest are given, and numerical solutions to these parameters for arbitrary propagation direction and two types of inhomogeneity of the medium are presented.     

Sound speed in extended Chaplygin fluid

We consider an extended Chaplygin gas equation of state which is driven from D-brane action and construct a cosmological model based on this equation of state. In this regard, we compute the scale factor of the model under a certain approximation. The conservation equation of this case is a non-linear differential equation which should solve using the special conditions. We also analyze the stability of the model by using sound speed as well as adiabatic index and discuss certain special cases of the model. We find special equation of state in this model which yields to dynamical and thermodynamical stability. Furthermore, we study the cosmological consequences of this model under certain conditions.     

Closed-form expressions for the rate of growth of perturbations in zero-pressure Friedmann-Lemaître universes

The general solutions to the density perturbation equation derived by Bonnor are pressented for the zero-pressure Friedmann-Lemaître universes in terms of elliptic functions. The particular solutions already published to this equation in terms of elementary functions are exhibited as special cases arising from the general solutions. These occur when the elliptic functions simplify to either trigonometric or hyperbolic functions.     

Bianchi type-II,VIII, and IX cosmological models with matter and electromagnetic fields

We present analytic solutions of the Einstein-Maxwell equations for cosmological models of LRS Bianchi type-II, VIII, and IX. The solutions represent anisotropic universes with source-free electromagnetic fields and perfect fluids matter satisfying the equation of state that is a function of the cosmic-time. Some physical properties of the models have been discussed.     

Charged anisotropic models for quark stars

We perform a detailed physical analysis for a class of exact solutions for the Einstein–Maxwell equations. The linear equation of state consistent with quark stars has been incorporated in the model. The physical analysis of the exact solutions is performed by considering the charged anisotropic stars for the particular nonsingular exact model obtained by Maharaj, Sunzu and Ray. In performing such an analysis we regain masses obtained by previous researchers for isotropic and anisotropic matter. It is also indicated that other masses and radii may be generated which are in acceptable ranges consistent with observed values of stellar objects. A study of the mass-radius relation indicates the effect of the electromagnetic field and anisotropy on the mass of the relativistic star.     

Shear-free and cavity models with plane symmetry

This paper aims to explore anisotropic planar analytical models for dissipative as well as non-dissipative matter distributions. We relate the Weyl tensor and physical variables of matter distribution. Darmois junction conditions are formulated on internal and external hypersurfaces. It is found that our dissipative models show the presence of cavity with non-zero expansion. Finally, we investigate two types of solutions with zero shear as well as heat flux by a specific choice of the mass function and by restricting pressure.     

Non-singular Bianchi-Kantowski-Sachs perfect fluid solutions of no-scale supergravity

We investigate the perfect fluid field equations of the Bianchi-Kantowski-Sachs models on the basis ofN=1 no-scale supergravity. A wide class of non-singular solutions is given in the stiff matter as well as in the radiation-dominated case. The vacuum solutions are included as special cases. The solutions given are of much interest in connection with the low-energy approximation of superstrings.     

Interacting dark matter and holographic dark energy in an anisotropic universe

In this paper we have studied the anisotropic and homogeneous Bianchi type-I universe filled with interacting Dark matter and Holographic dark energy. Here we discussed two models, in first model the solutions of the field equations are obtained for constant value of deceleration parameter where as in the second model the solutions of the field equations are obtained for special form of deceleration parameter. It is shown that for suitable choice of interaction between dark matter and holographic dark energy there is no coincidence problem (unlike ΛCDM). Also, in all the resulting models the anisotropy of expansion dies out very quickly and attains isotropy after some finite time. The Statefinder diagnostic is applied to both the models in order to distinguish between our dark energy models with other existing dark energy models. The physical and geometrical aspects of the models are also discussed.     

Exact anisotropic polytropic cylindrical solutions

In this paper, we study anisotropic compact stars with static cylindrically symmetric anisotropic matter distribution satisfying polytropic equation of state. We formulate the field equations as well as the corresponding mass function for the particular form of gravitational potential \(z(x)=(1+bx)^{\eta }~(\eta =1,~2,~3)\) and explore exact solutions of the field equations for different values of the polytropic index. The values of arbitrary constants are determined by taking mass and radius of compact star (Her X-1). We find that resulting solutions show viable behavior of physical parameters (density, radial as well as tangential pressure, anisotropy) and satisfy the stability condition. It is concluded that physically acceptable solutions exist only for \(\eta =1,~2\).     

SCR Steady State Distribution Function and Scattering Properties of the Interplanetary Medium

The propagation of energetic particles in the interplanetary space is considered on the basis of kinetic equation describing the scattering of charged particles by magnetic irregularities and the particle focusing by regular magnetic field. Our analysis confirms that angular distribution of solar cosmic rays contains a valuable information about properties of the particle scattering in the interplanetary magnetic field. Steady state solutions of the kinetic equation are applied to the analysis of solar proton events.