The different kinds of self-similarity in general relativity are discussed, with special emphasis
on similarity of thefirst'kind, corresponding to spacetimes admitting a homothetic vector. We …

This article is a guide to theorems on existence and global dynamics of solutions of the
Einstein equations. It draws attention to open questions in the field. The local-in-time Cauchy …

Dynamical systems theory is especially well-suited for determining the possible asymptotic
states (at both early and late times) of cosmological models, particularly when the governing …

Spatially homogeneous cosmological models with a positive cosmological constant are
investigated, using dynamical systems methods. We focus on the future evolution of these …

We perform a detailed dynamical analysis of anisotropic scalar-field cosmologies, and in
particular of the most significant Kantowski–Sachs, locally rotationally symmetric (LRS) …

In this paper, the gravitational field equations for static spherically symmetric perfect fluid
models with a polytropic equation of state, p= kρ1+ 1/n, are recast into two complementary 3 …

We discuss dynamical systems approaches and methods applied to flat Robertson-Walker
models in f (R)-gravity. We argue that a complete description of the solution space of a …

We study the spherical collapse of a perfect fluid with an equation of state P= k ρ by full
general relativistic numerical simulations. For 0< k≲ 0. 0 3 6, it has been known that there …

Scalar field cosmologies with a generalized harmonic potential and a matter fluid with a
barotropic Equation of State (EoS) with barotropic index γ for locally rotationally symmetric …

Abstract We investigate Kantowski-Sachs models in Einstein-æ ther theory with a perfect
fluid source using the singularity analysis to prove the integrability of the field equations and …