
Abstract 
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 
Wavemap
structure 

6.4 
Conserved quantities, kinetic energy density 
7 
Singularity,
Polarized Case 

7.1 
Equations, polarized T^{3}Gowdy 

7.2 
Associated Velocity
Term Dominated system 

7.3 
Asymptotics of the solution to the polarized
T^{3}Gowdy equations 

7.4 
Curvature blow up, polarized T^{3}case 

7.5 
Asymptotic
velocity, polarized T^{3}case 

7.6 
S^{2} × S^{1} and S^{3} cases 
8 
Asymptotic Expansions
Using Fuchsian Methods, General T^{3}Case 

8.1 
Geometric interpretation of
v_{a} 

8.2 
Restriction on the velocity 

8.3 
Geodesic loop 

8.4 
Existence of expansions
using Fuchsian methods, T^{3}case 

8.5 
Existence of expansions using Fuchsian
methods, S^{2} × S^{1} and S^{3} 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 T^{3}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 T^{3}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
T^{3}case 
15 
Acknowledgments 

References 

Figures 