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Divided into four parts, this book covers recent developments in topics pertaining to gravity theories, including discussions on the presence of scalar fields. Part One is devoted to exact solutions in general relativity, and is mainly concerned with the results of rotating null dust beams and fluids. Also included is a panoramic vision of new research directions in this area, which would require revising certain theorems and their possible extensions within gravity theories, new aspects concerning the Ernst potentials, double Kerr spacetimes, and rotating configurations. In particular, there is a detailed discussion of totally symmetric and totally geodesic spaces, in which a method for generating (2+1)-dimensional solutions from (3+1)-dimensional solutions is given. Part Two deals with alternative theories of gravity, all of which include scalar fields and gauge fields. Here, quantum and cosmological effects, which arise from both gravity theories in four and higher dimensions and from metric-affine theories, are investigated. Part Three is devoted to cosmological and inflationary scenarios. Local effects, such as the influence of scalar fields in protogalactic interactions, numerical studies of the collapse of molecular cores, as well as the inverse inflationary problem and the blue eigenvalue spectrum of it, are considered. Moreover, the role of scalar fields as dark matter and quantum cosmology in the Bergman-Wagoner and Gowdy theories, together with the relation of the conformal symmetry and deflationary gas universe, are likewise presented. The last part of the book includes some mixed topics which are still in the experimental stage. Among them are the foundation of the Maxwell theory, a discussion on electromagnetic Thirring problems, a note on the staticity of black holes with non-minimally coupled scalar fields, and a study of the Lorentz force free charged fluids in general relativity. Thus, this book is the most up-to-date, comprehensive collection of papers on the subject of exact solutions and scalar fields in gravity and is a valuable tool for researchers in the area.
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.
This volume is the refereed proceedings of the Sixth Canadian Conference on General Relativity and Relativistic Astrophysics held in May 1995 at the University of New Brunswick. The book includes invited talks and contributed talks and posters including state-of-the-art reviews of many of the most recent important developments in gravitational physics. This book would serve as a good supplement to standard texts on the topic. It features: review articles in key areas - black holes, numerical relativity, etc.; contributions covering most of gravitational physics; useful articles for students who wish to begin exploring the issues discussed; and, invited talks given by researchers known for their ability to communicate their expertise.
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.
A solution of the Einstein equations is by definition cosmological if it can reproduce the Friedmann (1922, 1924), Lemaitre (1927, 1931), Robertson (1929, 1933), and Walker (1935) (FLRW) metric by taking limiting values of arbitrary constants or functions. It has been a conventional wisdom in cosmology that the FLRW models successfully describe the large scale properties of our observed Universe, even since the 1930ies.
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.