Related papers: Self-similar Bianchi models: II. Class B models
In this paper we provide a classification of plane symmetric kinematic self-similar perfect fluid and dust solutions. In the perfect fluid and dust cases, kinematic self-similar vectors for the tilted, orthogonal and parallel cases have…
We use the dynamical systems approach to investigate the Bianchi type VIII models with a tilted $\gamma$-law perfect fluid. We introduce expansion-normalised variables and investigate the late-time asymptotic behaviour of the models and…
We consider vacuum anisotropic spatially homogeneous models in certain modified gravity theories (such as Ho\v{r}ava-Lifshitz, $\lambda$-$R$ or $f(R)$ gravity), which are expected to describe generic spacelike singularities for these…
Methods and properties regarding the linear perturbations are discussed for some spatially closed (vacuum) solutions of Einstein's equation. The main focus is on two kinds of spatially locally homogeneous solution; one is the Bianchi III…
In this paper, the crucial phenomenon of the expansion of the universe has been discussed. For this purpose, we study the vacuum solutions of Bianchi types $I$ and $V$ spacetimes in the framework of $f(R)$ gravity. In particular, we find…
We study perfect fluid cosmological models with a constant equation of state parameter $\gamma$ in which there are two naturally defined time-like congruences, a geometrically defined geodesic congruence and a non-geodesic fluid congruence.…
We consider a self-consistent system of Bianchi type-I (BI) gravitational field and a binary mixture of perfect fluid and dark energy given by a cosmological constant. The perfect fluid is chosen to be the one obeying either the usual…
The dynamics of cosmological models with isotropic matter sources (perfect fluids) is extensively studied in the literature; in comparison, the dynamics of cosmological models with anisotropic matter sources is not. In this paper we…
We study `purely radiative' (div E = div H = 0) and geodesic perfect fluids with non-constant pressure and show that the Bianchi class A perfect fluids can be uniquely characterized --modulo the class of purely electric and…
We study the Einstein field equations for spacetimes admitting a maximal two-dimensional abelian group of isometries acting orthogonally transitively on spacelike surfaces and, in addition, with at least one conformal Killing vector. The…
Symmetry assumptions on the geometrical framework have provided successful mechanisms to develop physically meaningful solutions to many problems. In tele-parallel gravity, invariance of the frame and spin-connection under a group of…
Spatially homogeneous and anisotropic Bianchi type V space-time with bulk viscous fluid source and time varying gravitational constant $G$ and cosmological term $\Lambda$ are considered. Coefficient of bulk viscosity $\zeta$ is assumed as a…
This paper is devoted to classify the most general plane symmetric spacetimes according to kinematic self-similar perfect fluid and dust solutions. We provide a classification of the kinematic self-similarity of the first, second, zeroth…
We find instanton/cosmological solutions with biaxial Bianchi-IX symmetry, involving non-trivial spatial dependence of the $\bbbc P^{1}$- and $\bbbc P^{2}$-sigma-models coupled to gravity. Such manifolds arise in N=1, $d=4$ supergravity…
We consider the late time behaviour of non-tilted perfect fluid Bianchi VII_0 models when the source is a radiation fluid, thereby completing the analysis of the Bianchi VII_0 models initiated by Wainwright et al in a recent paper. The…
In this paper we utilize symmetries in order to exhibit exact solutions to Einstein's equation of a perfect fluid on a static manifold all of whose spatial factor belongs to the conformal class of a Riemannian space of constant curvature.
The Bianchi type $\mathrm{VI}_{-1/9}$, $\mathrm{VIII}$ and $\mathrm{IX}$ vacuum models all have 4-dimensional Hubble-normalized state spaces and are expected to have a generic initial oscillatory singularity, but the invariant boundary sets…
We examine the behaviour of homogeneous, anisotropic space-times, specifically the locally rotationally symmetric Bianchi types $I$ and $VII_o$ in the presence of anisotropic matter. By finding an appropriate constant of the motion, and…
We study integrability by quadrature of a spatially flat Friedmann model containing both a minimally coupled scalar field $\phi$ with an exponential potential $V(\phi)\sim\exp[-\sqrt{6}\sigma\kappa\phi]$, $\kappa=\sqrt{8\pi G_N}$, of…
Perfect fluid with kinematic self-similarity is studied in 2+1 dimensional spacetimes with circular symmetry, and various exact solutions to the Einstein field equations are given. In particular, these include all the solutions of dust and…