A general introduction to the initial value problem for Einstein's equations coupled to collisionless matter. The book contains a proof of future stability of models of the universe consistent with the current observational data and a discussion of the restrictions on the possible shapes of the universe imposed by observations.
A general introduction to the initial value problem for Einstein's equations coupled to collisionless matter. The book contains a proof of future stability of models of the universe consistent with the current observational data and a discussion of the restrictions on the possible shapes of the universe imposed by observations.
Hans Ringström obtained his PhD in 2000 at the Royal Institute of Technology in Stockholm. He spent 2000-2004 as a post doc in the Max Planck Institute for Gravitational Physics, also known as the Albert Einstein Institute. In 2004 he returned to Stockholm as a research assistant. In 2007 he became a Royal Swedish Academy of Sciences Research Fellow, supported by a grant from the Knut and Alice Wallenberg Foundation, a position which lasted until 2012. In 2011, Ringström obtained an associate professorship at the Royal Institute of Technology.
Inhaltsangabe
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 Non-Degenerate Minimum 28: Approximating Fluids VIII Future Global Non-Linear 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, Einstein-Boltzmann
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 Non-Degenerate Minimum 28: Approximating Fluids VIII Future Global Non-Linear 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, Einstein-Boltzmann
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