Inhomogeneous generalization of some Bianchi models

Vacuum Bianchi models which can be transformed to the Einstein-Rosen metric are considered. The models are used in order to construct new inhomogeneous universes, which are generalizations of Bianchi cosmologies of types III, V and VI_h. Recent generalizations of these Bianchi models, considered by Wainwright et al., are also discussed.     

Inhomogeneous cosmologies: The cosmic peeling-off property of gravity

Asymptotic expansions are used to study the late-time behavior of the Riemann tensor for a large class of inhomogeneous cosmological models. These models include the unidirectional inhomogeneous generalizations of Bianchi type I–VII universes. The cosmic analog of the peeling-off theorem, familiar from general relativity, is formulated. It is also shown that chaotic behavior near the initial singularity transforms itself into pure gravitational radiation at late times.     

Bianchi Type-II, VIII & IX Cosmological Models with Strange Quark Matter Attached to String Cloud in Brans–Dicke and General Theory of Gravitation

We have obtained and presented spatially homogeneous Bianchi type-II, VIII & IX cosmological models with strange quark matter attached to string cloud in Brans and Dicke (Phys. Rev. C 71:054905, 1961) scalar tensor theory and general theory of gravitation. Some important features of the models, thus obtained, have been discussed. We noticed that these universes always expand isotropically and the presence of scalar field doesn’t affect the geometry of the space-time but changes the matter distribution.     

N-dimensional non-abelian dilatonic,stable black holes and their Born–Infeld extension

We find large classes of non-asymptotically flat Einstein–Yang–Mills–Dilaton and Einstein–Yang–Mills–Born–Infeld–Dilaton black holes in N-dimensional spherically symmetric spacetime expressed in terms of the quasilocal mass. Extension of the dilatonic YM solution to N-dimensions has been possible by employing the generalized Wu-Yang ansatz. Another metric ansatz, which aided in finding exact solutions is the functional dependence of the radius function on the dilaton field. These classes of black holes are stable against linear radial perturbations. In the limit of vanishing dilaton we obtain Bertotti–Robinson type metrics with the topology of AdS ₂×S ^N–2. Since connection can be established between dilaton and a scalar field of Brans–Dicke type we obtain black hole solutions also in the Brans–Dicke–Yang–Mills theory as well.     

Homogeneous Bianchi type VI0 perfect fluid space-times

An algorithm is presented for generating new exact solutions of the Einstein equations for spatially homogeneous cosmological models of Bianchi type VI₀. The energy-momentum tensor is of perfect fluid type. Starting from Dunn and Tupper's dust-filled universe, new classes of solutions are obtained. The solutions represent anisotropic universes filled with perfect fluid not satisfying the equation of state. Some of their physical properties are studied.     

Bianchi type-I,V and VIo models in modified generalized scalar-tensor theory

In modified generalized scalar-tensor (GST) theory, the cosmological term Λ is a function of the scalar field ϕ and its derivatives . We obtain exact solutions of the field equations in Bianchi Type-I, V and VIo space-times. The evolution of the scale factor, the scalar field and the cosmological term has been discussed. The Bianchi Type-I model has been discussed in detail. Further, Bianchi Type-V and VIo models can be studied on the lines similar to Bianchi Type-I model.      

Survey of cosmological models with gravitational,scalar and electromagnetic waves

This paper gives an overview and reviews some recent investigations of anisotropic and inhomogeneous models. A class of models, which admit an Abelian two-parameter group of isometries, is considered in detail. Within this class of models we present exact solutions of the Einstein field equations. These solutions describe inhomogeneous cosmological models containing gravitational, scalar and electromagnetic waves. The solutions are used to study the effect of the symmetry breaking in corresponding Bianchi models. The nonlinear dynamics of primordial inhomogeneities is considered. The global evolution of the inhomogeneous models considered is also investigated. Finally we discuss the validity of various assumptions, used in the earlier treatments of inhomogeneous models.     

Some Anisotropic Universes in the Presence of Imperfect Fluid Coupling with Spatial Curvature

We consider Bianchi VI spacetime, which also can be reduced to Bianchi types VI₀-V-III-I. We initially consider the most general form of the energy-momentum tensor which yields anisotropic stress and heat flow. We then derive an energy-momentum tensor that couples with the spatial curvature in a way so as to cancel out the terms that arise due to the spatial curvature in the evolution equations of the Einstein field equations. We obtain exact solutions for the universes indefinitely expanding with constant mean deceleration parameter. The solutions are beriefly discussed for each Bianchi type. The dynamics of the models and fluid are examined briefly, and the models that can approach to isotropy are determined. We conclude that even if the observed universe is almost isotropic, this does not necessarily imply the isotropy of the fluid (e.g., dark energy) affecting the evolution of the universe within the context of general relativity.     

Electromagnetic Bianchi cosmologies

All exact solutions of the Einstein-Maxwell equations of Bianchi type-I which are of physical importance have been found. The solutions represent non-locally rotationally symmetric universes with source-free electromagnetic fields and the matter content is a perfect fluid, with equation of state p=(γ?1)?(1?γ?2). Non-titled Bianchi type-II models are integrated for perfect fluid matter for all values of γ.     

Homogeneous anisotropic cosmological models with viscous fluid and magnetic field

The paper presents some exact solutions of Bianchi types I and III and Kantowski-Sachs cosmological models consisting of a dissipative fluid along with an axial magnetic field. A barytropic equation of state (p=), together with a pair of linear relations between the matter density (), the shear scalar (), and the expansion scalar () have been assumed for simplicity. The solutions are basically of two different types, one for the Bianchi I and the other for III and Kantowski-Sachs type. The presence of the magnetic field, however, does not change the fundamental nature of the initial singularity.     

Gravitational fields with space-times of Bianchi type IX

Spatially homogeneous space-times of Bianchi type IX are considered. A general scheme for the derivation of exact solutions of Einstein’s equations corresponding to perfect fluid plus pure radiation fields is outlined. Some simple rotating Bianchi type IX cosmological models are presented. The details of these solutions are also discussed. The authors felicitate Prof. D S Kothari on his eightieth birthday and dedicate this paper to him on this occasion.     

Isotropisation of flat homogeneous Bianchi type <Emphasis Type="Italic">I</Emphasis> model with a non minimally coupled and massive scalar field

In previous works, we studied the isotropisation of some Bianchi class A models with a minimally coupled scalar field. In this paper we extend these results, in the special case of a Bianchi type I model, to a non minimally coupled scalar field. The Universe isotropisation for the Brans-Dicke and low energy string theories are studied.     

Scalar field cosmologies in a Bianchi type I universe

The dynamics of a homogeneous, anisotropic, spatially flat Bianchi type I universe filled with a scalar field is studied. Using the usual synchronous form of the line element, general exact solutions for the Einstein field equations are obtained in the case of the exponential-potential scalar field (V=Λexp(k?)) and in the case of the Barrow-Saich potential ( $V \sim \dot \varphi ^2 $ ). Conditions under which inflation can occur are discussed and the late-time behaviour of the models is also considered.     

Plane Symmetric Vacuum Bianchi Type <Emphasis Type="Italic">III</Emphasis> Cosmology in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) Gravity

The main purpose of this paper is to study the exact solution of Bianchi type III spacetime in the context of metric f(R) gravity. The field equations are solved by taking expansion scalar θ proportional to shear scalar σ which gives C=A ⁿ , where A and C are the metric coefficients. The physical behavior of the solution has been discussed using some physical quantities. Also, the function of the Ricci scalar is evaluated.     

Bulk Viscous Bianchi Type V Cosmological Models with Decaying Cosmological Term Λ

We present bulk viscous Bianchi type V cosmological models with time-dependent cosmological term Λ. Exact solutions of Einstein field equations have been obtained by assuming shear scalar σ proportional to volume expansion θ. The coefficient of bulk viscosity is taken to be power function of energy density ρ or volume expansion θ. In these models cosmological term Λ come out to be negative. It is found that models obtained are expanding, shearing and non-rotating. They do not approach isotropy for large values of time t. Some observational parameters for the model have also been discussed.     

Hopf Solitons and Area-Preserving Diffeomorphisms of the Sphere

We consider a (3+1)-dimensional local field theory defined on the sphere S ². The model possesses exact soliton solutions with nontrivial Hopf topological charges and an infinite number of local conserved currents. We show that the Poisson bracket algebra of the corresponding charges is isomorphic to that of the area-preserving diffeomorphisms of the sphere S ². We also show that the conserved currents under consideration are the Noether currents associated to the invariance of the Lagrangian under that infinite group of diffeomorphisms. We indicate possible generalizations of the model.     

Non-vacuum Bianchi types <Emphasis Type="Italic">I</Emphasis> and <Emphasis Type="Italic">V</Emphasis> in <Emphasis Type="Italic">f</Emphasis> (<Emphasis Type="Italic">R</Emphasis>) gravity

In a recent paper (Sharif and Shamir in Class. Quantum Grav. 26:235020, 2009), we have studied the vacuum solutions of Bianchi types I and V spacetimes in the framework of metric f (R) gravity. Here we extend this work to perfect fluid solutions. For this purpose, we take stiff matter to find energy density and pressure of the universe. In particular, we find two exact solutions in each case which correspond to two models of the universe. The first solution gives a singular model while the second solution provides a non-singular model. The physical behavior of these models has been discussed using some physical quantities. Also, the function of the Ricci scalar is evaluated.     

Entropies of a Toroidal Black Hole Due to Scalar and Dirac Fields

Using the thin film brick-wall model, the entropies of a toroidal black hole due to scalar and Dirac fields are investigated. The entropy due to the scalar field is one fourth of the horizon area, and that due to the Dirac field is seven eighth of the area. These results are similar to that in black holes with horizon topology S ². The cutoff in toroidal black hole is chosen as the same as one in black holes with horizon topology S ², which seems to mean that the thin film brick-wall model is universal.     

Ψ=We ±Φ Quantum cosmological solutions for class A Bianchi models

We find exact solutions to the Wheeler-DeWitt equation, for a certain factor ordering. They have the form =We ^± for class A Bianchi models, where is a solution to the classical Hamilton-Jacobi equation, generalizing the only known solution of Moncrief and Ryan for the Bianchi type IX model in standard quantum cosmology. The same kind of solution has also been found in supersymmetric quantum cosmology.     

Collision-free gases in Bianchi space-times

We study collision-free gases in Bianchi space-times. Spatially homogeneous distribution functions are found for all Bianchi types by supposing that the distribution functionf(x, p) is a function of the Killing vector constants of the motion only. Bianchi types I, VIII and IX only, lead to physical distributions. In types VIII and IX the average behaviour of the gas is that of a nonrotating viscous fluid. In an attempt to obtain physical spatially homogeneous distribution functions for all Bianchi types, we write the Liouville equation in a spatially homogeneous orthonormal tetrad. Furthermore, the general inhomogeneous solution of Liouville's equation in Bianchi type I is obtained, depending on constants of the motion that generalise the conserved quantities generated by Lorentz boosts in flat space-time.