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In this thesis we first give a brief introduction to the application of dynamical systems to cosmology. This enables us to study spherically-symmetric cosmological models in Einstein-aether theory with a scalar field. The models depend on the time-like aether vector field through the expansion and shear scalars, and we focus on some special cases of the models. This leads to a compact phase space. From the evolution equations we obtain a three-dimensional dynamical system in terms of expansion-normalized variables. The aim of studying this system is to find the local stability of the equilibrium points of the dynamical system corresponding to physically realistic solutions. As an application we study spherically symmetric Einstein-aether Kantowski-Sachs cosmological models with a scalar field using the dynamical systems theory.
The aim of this work is to provide a proof of the nonlinear gravitational stability of the Minkowski space-time. More precisely, the book offers a constructive proof of global, smooth solutions to the Einstein Vacuum Equations, which look, in the large, like the Minkowski space-time. In particular, these solutions are free of black holes and singularities. The work contains a detailed description of the sense in which these solutions are close to the Minkowski space-time, in all directions. It thus provides the mathematical framework in which we can give a rigorous derivation of the laws of gravitation proposed by Bondi. Moreover, it establishes other important conclusions concerning the nonlinear character of gravitational radiation. The authors obtain their solutions as dynamic developments of all initial data sets, which are close, in a precise manner, to the flat initial data set corresponding to the Minkowski space-time. They thus establish the global dynamic stability of the latter. Originally published in 1994. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
The so-called Einstein-Aether theory is General Relativity coupled (at second derivative order) to a dynamical time-like unit vector field (the "Aether"). It is a Lorentz-violating theory and has gained much attention in recent years. We study two classes of Einstein-Aether cosmological scalar field models using dynamical systems techniques. In particular, we are interested in exploring the impact of Lorentz violation on the inflationary scenario. We study the local stability of the equilibrium points of the dynamical system corresponding to physically realistic solutions and find that there are always ranges of values of the parameters of the models for which there exists an inflationary attractor. In the first application, we investigate the qualitative behaviour of a class of spatially homogeneous Einstein-Aether models with a scalar field. Particularly, we study two models; an isotropic model and an anisotropic model. In both models there always exists a range of the values of the parameters in which there is an attractor which corresponds to an inflationary universe at late times. In the second application, we study spherically symmetric cosmological models with a scalar field. Particularly, we consider a special case of spatially homogeneous Kantowski-Sachs models using appropriate normalized bounded variables. In this special case, we found that there always exists a range of values in the parameters in which there is one inflationary attractor solution which corresponds to an inflationary of the Universe at late times.
"Astronomy and Astrophysics Abstracts" appearing twice a year has become oneof the fundamental publications in the fields of astronomy, astrophysics andneighbouring sciences. It is the most important English-language abstracting journal in the mentioned branches. The abstracts are classified under more than a hundred subject categories, thus permitting a quick survey of the whole extended material. The AAA is a valuable and important publication for all students and scientists working in the fields of astronomy and related sciences. As such it represents a necessary ingredient of any astronomical library all over the world.
This work examines the mathematical aspects of nonlinear wave propagation, emphasizing nonlinear hyperbolic problems. It introduces the tools that are most effective for exploring the problems of local and global existence, singularity formation, and large-time behaviour of solutions, and for the study of perturbation methods.