Living Reviews in Relativity

"Cosmic Censorship for Gowdy Spacetimes"
Hans Ringström  

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1 Introduction and Outline
1.1 Outline, basic material
1.2 Outline, the asymptotics in the direction towards the singularity
1.3 Outline, the expanding direction
1.4 Strong cosmic censorship
2 Gowdy Spacetimes
2.1 Symmetry in cosmology
2.2 Definition of the Gowdy class
2.3 Coordinate systems
2.4 The polarized subcase
3 Foliations
3.1 CMC foliations
3.2 Areal foliation
3.3 Existence of foliations, related symmetry classes
3.4 Prescribed mean curvature
4 Strong Cosmic Censorship
4.1 The initial value problem
4.2 Strong cosmic censorship
4.3 Curvature blow up
4.4 Pathological examples in the case of Gowdy
5 BKL, Fuchsian Methods and Asymptotic Expansions
5.1 The BKL picture
5.2 Asymptotic expansions, Fuchsian methods
6 Equations
6.1 Expanding direction
6.2 The direction towards the singularity
6.3 Wave-map structure
6.4 Conserved quantities, kinetic energy density
7 Singularity, Polarized Case
7.1 Equations, polarized T3-Gowdy
7.2 Associated Velocity Term Dominated system
7.3 Asymptotics of the solution to the polarized T3-Gowdy equations
7.4 Curvature blow up, polarized T3-case
7.5 Asymptotic velocity, polarized T3-case
7.6 S2 × S1 and S3 cases
8 Asymptotic Expansions Using Fuchsian Methods, General T3-Case
8.1 Geometric interpretation of va
8.2 Restriction on the velocity
8.3 Geodesic loop
8.4 Existence of expansions using Fuchsian methods, T3-case
8.5 Existence of expansions using Fuchsian methods, S2 × S1 and S3 cases
9 Spikes
9.1 Inversion
9.2 Gowdy to Ernst transformation
9.3 False spikes
9.4 High velocity spikes
10 Asymptotic Velocity, General T3-Gowdy
10.1 Existence of an asymptotic velocity
10.2 Relevance of the asymptotic velocity to the issue of curvature blow up
10.3 Interpretation of the asymptotic velocity as a rate of convergence to the boundary in hyperbolic space
10.4 Two dimensional version of the asymptotic velocity
10.5 Dominant contribution to the asymptotic velocity
10.6 Value of the asymptotic velocity as a criterion for the existence of expansions
11 The Generic Set, General T3-Gowdy
11.1 Nondegenerate true spikes
11.2 Nondegenerate false spikes
11.3 The generic set, definition
11.4 Verification of genericity, openness
11.5 Verification of genericity, density
12 Expanding Direction, Polarized Gowdy
12.1 Asymptotic behavior
12.2 Comparison with spatially homogeneous solutions
13 Expanding Direction, The General Case
13.1 Energy decay
13.2 Proof of decay of the energy
13.3 Asymptotic ODE behavior
13.4 Geometric interpretation of the asymptotics
13.5 Concluding remarks
13.6 Geodesic completeness
14 Strong Cosmic Censorship in Gowdy Spacetimes
14.1 The polarized case
14.2 General T3-case
15 Acknowledgments
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