Related papers: Integrability and explicit solutions in some Bianc…
The Einstein field equations for a class of irrotational non-orthogonally transitive $G_{2}$ cosmologies are written down as a system of partial differential equations. The equilibrium points are self-similar and can be written as a…
Bianchi type V string cosmological models in general relativity are investigated. To get the exact solution of Einstein's field equations, we have taken some scale transformations followed by Camci $\it et ~ al$ (2001). It is shown that…
We study integrable models in the Bianchi I metric case with scalar fields minimally and non-minimally coupled with gravity and the correspondence between their general solutions. Using the model with a minimally coupled scalar field and a…
Centre manifold theory is applied to some dynamical systems arising from spatially homogeneous cosmological models. Detailed information is obtained concerning the late-time behaviour of solutions of the Einstein equations of Bianchi type…
Some exact solutions for the Einstein field equations corresponding to inhomogeneous $G_2$ cosmologies with an exponential-potential scalar field which generalize solutions obtained previously are considered. Several particular cases are…
To analyze linear field equations on a locally homogeneous spacetime by means of separation of variables, it is necessary to set up appropriate harmonics according to its symmetry group. In this paper, the harmonics are presented for a…
The theory of symmetries of systems of coupled, ordinary differential equations (ODE) is used to develop a concise algorithm in order to obtain the entire space of solutions to vacuum Bianchi Einstein Field Equations (EFEs). The symmetries…
The second order Ordinary Differential Equation which describes the unknown part of the solution space of some vacuum Bianchi Cosmologies is completely integrated for Type III, thus obtaining the general solution to Einstein's Field…
Einstein's field equations for stationary Bianchi type II models with a perfect fluid source are investigated. The field equations are rewritten as a system of autonomous first order differential equations. Dimensionless variables are…
In this work, we are investigating the problem of integrability of Bianchi class A cosmological models. This class of systems is reduced to the form of Hamiltonian systems with exponential potential forms. The dynamics of Bianchi class A…
In this thesis we investigate cosmological models more general than the isotropic and homogeneous Friedmann-Lemaitre models. We focus on cosmologies with one spatial degree of freedom, whose matter content consists of a perfect fluid and…
The general exact solution of the Einstein-Dirac equations with cosmological constant in the homogeneous Riemannian space of the Bianchi 1 type is obtained.
We study time-dependent compactification of extra dimensions. We assume that the spacetime is spatially homogeneous, and solve the vacuum Einstein equations without cosmological constant in more than three dimensions. We consider globally…
To understand the observational properties of cosmological models, in particular, the temperature of the cosmic microwave background radiation, it is necessary to study their null geodesics. Dynamical systems theory, in conjunction with the…
In this thesis we consider several aspects of general relativity relating to exact solutions of the Einstein equations. In the first part gravitational plane waves in the Rosen form are investigated, and we develop a formalism for writing…
We investigate the dynamics of spatially homogeneous solutions of the Einstein-Vlasov equations with Bianchi type I symmetry by using dynamical systems methods. All models are forever expanding and isotropize toward the future; toward the…
We present a general solution-generating result within the bidifferential calculus approach to integrable partial differential and difference equations, based on a binary Darboux-type transformation. This is then applied to the…
The Gowdy cosmologies are vacuum solutions to the Einstein equations which possess two space-like Killing vectors and whose spatial sections are compact. We consider the simplest of these cosmological models: the case where the spatial…
In this work we construct an effective four-dimensional model by compactifying a ten-dimensional theory of gravity coupled with a real scalar dilaton field on a time-dependent torus. The corresponding action in four dimensions is similar to…
We present new exact inhomogeneous vacuum cosmological solutions of Einstein's equations. They provide new information about the nature of general cosmological solutions to Einstein's equations.