Hans Ringström
On the Topology and Future Stability of the Universe
Hans Ringström
On the Topology and Future Stability of the Universe
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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.
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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.
Produktdetails
- Produktdetails
- Oxford Mathematical Monographs
- Verlag: Oxford University Press, USA
- New
- Seitenzahl: 768
- Erscheinungstermin: 18. Juli 2013
- Englisch
- Abmessung: 236mm x 155mm x 43mm
- Gewicht: 1202g
- ISBN-13: 9780199680290
- ISBN-10: 0199680299
- Artikelnr.: 37313610
- Oxford Mathematical Monographs
- Verlag: Oxford University Press, USA
- New
- Seitenzahl: 768
- Erscheinungstermin: 18. Juli 2013
- Englisch
- Abmessung: 236mm x 155mm x 43mm
- Gewicht: 1202g
- ISBN-13: 9780199680290
- ISBN-10: 0199680299
- Artikelnr.: 37313610
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.
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
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
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