On the topology and future stability of the universe
 Responsibility
 Hans Ringström, Department of Mathematics, KTH Royal Institute of Technology, Sweden.
 Language
 English.
 Edition
 First edition.
 Publication
 Oxford, UK : Oxford University Press, 2013.
 Physical description
 xiv, 718 pages : illustrations (some color) ; 24 cm.
 Series

Oxford mathematical monographs.
Oxford science publications.
Access
Creators/Contributors
 Author/Creator
 Ringström, Hans, author.
Contents/Summary
 Bibliography
 Includes bibliographical references (pages 707713) and index.
 Contents

 I PROLOGUE  1. Introduction  2. The Initial Value Problem  3. The Topology of the Universe  4. Notions of Proximity  5. Observational Support  6. Concluding Remarks  II INTRODUCTORY MATERIAL  7. Main Results  8. Outline, General Theory  9. Outline, Main Results  10. References and Outlook  III BACKGROUND AND BASIC CONSTRUCTIONS  11. Basic Analysis Estimates  12. Linear Algebra  13. Coordinates  IV FUNCTION SPACES, ESTIMATES  14. Function Spaces, Distribution Functions  15. Function Spaces on Manifolds  16. Main Weighted Estimate  17. Concepts of Convergence  V LOCAL THEORY  18. Uniqueness  19. Local Existence  20. Stability  VI THE CAUCHY PROBLEM IN GENERAL RELATIVITY  21. The Vlasov Equation  22. The Initial Value Problem  23. Existence of an MGHD  24. Cauchy Stability  VII SPATIAL HOMOGENEITY  25. Spatially Homogeneous Metrics  26. Criteria Ensuring Global Existence  27. A Positive NonDegenerate Minimum  28. Approximating Fluids  VIII FUTURE GLOBAL NONLINEAR STABILITY  29. Background Material  30. Estimates for the Vlasov Matter  31. Global Existence  32. Asymptotics  33. Proof of the Stability Results  34. Models with Arbitrary Spatial Topology  IX APPENDICES  A. Pathologies  B. Quotients and Universal Covering Spaces  C. Spatially Homogeneous and Isotropic Metrics  D. Auxiliary Computations in Low Regularity  E. Curvature, Left Invariant Metrics  F. Comments, EinsteinBoltzmann.
 (source: Nielsen Book Data)
 Publisher's Summary
 The standard starting point in cosmology is the cosmological principle; the assumption that the universe is spatially homogeneous and isotropic. After imposing this assumption, the only freedom left, as far as the geometry is concerned, is the choice of one out of three permissible spatial geometries, and one scalar function of time. Combining the cosmological principle with an appropriate description of the matter leads to the standard models. It is worth noting that these models yield quite a successful description of our universe. However, even though the universe may, or may not, be almost spatially homogeneous and isotropic, it is clear that the cosmological principle is not exactly satisfied. This leads to several questions. The most natural one concerns stability: given initial data corresponding to an expanding model of the standard type, do small perturbations give rise to solutions that are similar to the future? Another question concerns the shape of the universe: what are the restrictions if we only assume the universe to appear almost spatially homogeneous and isotropic to every observer? The main purpose of the book is to address these questions. However, to begin with, it is necessary to develop the general theory of the Cauchy problem for the EinsteinVlasov equations. In order to to make the results accessible to researchers who are not mathematicians, but who are familiar with general relativity, the book contains an extensive prologue putting the results into a more general context.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2013
 Series
 Oxford mathematical monographs
 Oxford science publications
 ISBN
 9780199680290
 0199680299