Related papers: Integrability and explicit solutions in some Bianc…
We present a new generating algorithm to construct exact non static solutions of the Einstein field equations with two-dimensional inhomogeneity. Infinite dimensional families of $G_1$ inhomogeneous solutions with a self interacting scalar…
We characterize real elliptic differential systems whose solutions can be expressed in terms of holomorphic solutions to an associated holomorphic Pfaffian system $\mathcal H$ on a complex manifold. In particular, these elliptic systems…
We consider the Bianchi I geometry coupled to several species of comoving barotropic perfect fluids with a linear equation of state in the context of general relativity. The solution of the dynamics can be reduced to a quadrature, which can…
The dynamics and evolution of Bianchi type I space-times is considered in the framework of the four-dimensional truncation of a reduced theory obtained from the N=2,D=5 supergravity. The general solution of the gravitational field equations…
We construct a 4-parameter family of inhomogeneous cosmological models, which contains two recently derived 3-parameter families as special cases. The corresponding exact vacuum solution to Einstein's field equations is obtained with…
Einstein's field equations for spatially self-similar locally rotationally symmetric perfect fluid models are investigated. The field equations are rewritten as a first order system of autonomous ordinary differential equations.…
Bianchi type V perfect fluid cosmological models are investigated with cosmological term $\Lambda$ varying with time. Using a generation technique (Camci {\it et al.}, 2001), it is shown that the Einstein's field equations are solvable for…
Rigorous results on solutions of the Einstein-Vlasov system are surveyed. After an introduction to this system of equations and the reasons for studying it, a general discussion of various classes of solutions is given. The emphasis is on…
The Einstein-Vlasov-Fokker-Planck system describes the kinetic diffusion dynamics of self-gravitating particles within the Einstein theory of general relativity. We study the Cauchy problem for spatially homogeneous and isotropic solutions…
A discrete symmetry of the four-dimensional string effective action is employed to derive spatially homogeneous and inhomogeneous string cosmologies from vacuum solutions of general relativity that admit two commuting spacelike Killing…
The dynamics of a class of cosmological models with collisionless matter and four Killing vectors is studied in detail and compared with that of corresponding perfect fluid models. In many cases it is possible to identify asymptotic states…
Bianchi type V bulk viscous fluid cosmological models are investigated. Using a generation technique (Camci {\it et al.}, 2001), it is shown that the Einstein's field equations are solvable for any arbitrary cosmic scale function. The…
I give a compact, pedagogical review of our present understanding of the universe as based on general relativity. This includes the uniform models, with special reference to the cosmological 'constant'; and the equations for…
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…
We discuss an integrable discretization of the principal chiral field models equations and its involutive reduction. We present a Darboux transformation and general construction of solution solutions for these discrete equations.
The aim of these notes is to present an accessible overview of some topics in classical algebraic geometry which have applications to aspects of discrete integrable systems. Precisely, we focus on surface theory on the algebraic geometry…
We study a class of inhomogeneous and anisotropic $G_2$ string cosmological models. In the case of separable $G_2$ models we show that the governing equations reduce to a system of ordinary differential equations. We focus on a class of…
A multidimensional field model describing the behaviour of (at most) one Einstein space of non-zero curvature and n Ricci-flat internal spaces is considered. The action contains several dilatonic scalar fields and antisymmetric forms. The…
By viewing Einstein's field equations -- reduced to two dimensions -- as an integrable system, one can simultaneously obtain exact solutions to both the equations themselves and their associated Lax pair via a canonical Wiener-Hopf…
Cosmological models arising from a generalized compactification of Einstein gravity are derived. It is shown that a redefinition of the moduli fields reduces the system to a set of massless fields and a single field with a single…