Abelian G2 Cosmologies / Gowdy Vacuum Cosmologies

1. Gowdy R H: Gravitational Waves in Closed Universes, Phys. Rev. Lett. 27 (1971), 826
2. Gowdy R H: Vacuum Spacetimes and Compact Invariant Hyperspaces: Topologies and Boundary Conditions, Ann. Phys. (N.Y.) 83 (1974), 203
3. Wainwright J, S W Goode: Some Exact Inhomogeneous Cosmologies with Equation of State $p=\gamma\,\mu$, Phys. Rev. D 22 (1980), 1906
   NB: $\mu \ge p \ge 0$, $0 < \gamma < 1$, $\omega^{a}=0$; both KVF HSO and mutually orthogonal; separability ansatz employed; solution contains two constant essential parameters; $\mathbb{R}^{3}$ spatial topology; Petrov type I; models do not approach spatial homogeneity at large times or near the singularity and are not self-similar; $K = 0$ LRS subcase.
4. Kramer D: A New Inhomogeneous Cosmological Model in General Relativity, Class. Quantum Grav. 1 (1984), 611
   NB: Perfect fluid; non-orthogonally transitive symmetry group; $\gamma=2$ plus $\Lambda$ matter interpretation.
5. Hewitt C G, J Wainwright, S W Goode: Qualitative Analysis of a Class of Inhomogeneous Self-Similar Cosmological Models, Class. Quantum Grav. 5 (1988), 1313
   NB: Dynamical systems analysis of dynamical equilibrium states of diagonal $G_{2}$ perfect fluid class with $p(\mu) = (\gamma-1)\,\mu$, I: compact state space.
6. Feinstein A, J M M Senovilla: A New Inhomogeneous Cosmological Perfect Fluid Solution with $p=\mu/3$, Class. Quantum Grav. 6 (1989), L89
   NB: Follows the lines of Wainwright/Goode '80; very good introduction into the motivation for exact solutions of the EFE; $\sigma_{ab}$ degenerate in plane orthogonal to group orbits (PLRS); solution contains no free functions of $x$-coord but any one essential parameter $a = \mbox{constant}$; $\mathbb{R}^{3}$ spatial topology.
7. Hewitt C G, J Wainwright: Orthogonally Transitive $G_{2}$ Cosmologies, Class. Quantum Grav. 7 (1990), 2295
   NB: Contains a formal quasi-linear (non-symmetric) hyperbolic evolution system with frame derivatives for 9 expansion-normalised dependent variables (functions of local coordinates $t$ and $x$).
8. Isenberg J, M Jackson, V Moncrief: Evolution of the Bel-Robinson Energy in Gowdy $\mathbb{T}^{3}\times\mathbb{R}$ Space-times, J. Math. Phys. 31 (1990), 517
9. Isenberg J, V Moncrief: Asymptotic Behavior of the Gravitational Fields and the Nature of Singularities in Gowdy Spacetimes, Ann. Phys. (N.Y.) 199 (1990),84
   NB: Polarised Gowdy case only; establishes concept of "asymptotically velocity term dominated" singularities; employs method of "energy functionals" to prove existence theorems.
10. Senovilla J M M: New Class of Inhomogeneous Cosmological Perfect-Fluid Solutions without Big-Bang Singularity, Phys. Rev. Lett. 64 (1990), 2219
    NB: Both KVF HSO, so line element diagonal ("polarised" case); comoving coords; irrotational perfect fluid with $p=\mu/3$ (radiation); Petrov type I; $\sigma_{ab}$ degenerate in plane orthogonal to group orbits (PLRS); solution contains no free functions of $x$-coord but any one essential parameter $a = \mbox{constant}$; $\mathbb{R}^{3}$ spatial topology; change to cylindrically symmetrical $\mathbb{R}^{2}\times\mathbb{S}^{1}$ spatial topology discussed.
11. Wils P: A Class of Inhomogeneous Perfect Fluid Cosmologies, Class. Quantum Grav. 7 (1990), L43
    NB: $\xi_{\mu}\,\eta^{\mu}=0$.
12. Hewitt C G, J Wainwright, M Glaum: Qualitative Analysis of a Class of Inhomogeneous Self-Similar Cosmological Models: II, Class. Quantum Grav. 8 (1991), 1505
    NB: Dynamical systems analysis of dynamical equilibrium states of diagonal $G_{2}$ perfect fluid class with $p(\mu) = (\gamma-1)\,\mu$, II: non-compact state space.
13. Wils P: Inhomogeneous Perfect Fluid Cosmologies With A Non-Orthogonally Transitive Symmetry Group, Class. Quantum Grav. 8 (1991), 361
    NB: Irrotational; one KVF HSO.
14. Uggla C: Inhomogeneous Self-Similar Cosmological Models, Class. Quantum Grav. 9 (1992), 2287
    NB: $H_{3}$ transitive on timelike 3-surfaces; reduction of EFE to system of ODEs; Hamiltonian formulation; $p(\mu) = (\gamma-1)\,\mu$.
15. Van den Bergh N, J Skea: Inhomogeneous Perfect Fluid Cosmologies, Class. Quantum Grav. 9 (1992), 527
    NB: Both KVF HSO; $p=(\gamma-1)\,\mu$; models are asymptotically self-similar.
16. Patel L K, N Dadhich: Singularity-Free Inhomogeneous Models with Heat Flow, Class. Quantum Grav. 10 (1993), L85
17. Mars M: New Non-Separable Diagonal Cosmologies, Class. Quantum Grav. 12 (1995), 2831
    NB: Quotient of norms of the two orthogonal KVF constant along $u$.
18. Mars M, J M M Senovilla: Non-Diagonal $G_{2}$ Separable Perfect Fluid Spacetimes, Class. Quantum Grav. 14 (1997), 205
    NB: Orthogonally-transitive symmetry group; separation of variables assumed.
19. Senovilla J M M, R Vera: Dust $G_{2}$ Cosmological Models, Class. Quantum Grav. 14 (1997), 3481
20. Hern S D, J M Stewart: The Gowdy $\mathbb{T}^{3}$ Cosmologies Revisited, Class. Quantum Grav. 15 (1998), 1581. Also: Preprint gr-qc/9708038.
21. Hübner P: More about Vacuum Spacetimes with Toroidal Null Infinities, Class. Quantum Grav. 15 (1998), L21. Also: Preprint gr-qc/9708042.
22. Kichenassamy S, A D Rendall: Analytic Description of Singularities in Gowdy Spacetimes, Class. Quantum Grav. 15 (1998), 1339
    NB: Transforms EFE to a system of Fuchsian PDE for constructing singular solutions.
23. Senovilla J M M, R Vera: $G_{2}$ Cosmological Models Separable in Non-Comoving Coordinates, Class. Quantum Grav. 15 (1998), 1737. Also: Preprint gr-qc/9803069.
24. van Elst H, G F R Ellis, B G Schmidt: On the Propagation of Jump Discontinuities in Relativistic Cosmology, Preprint gr-qc/0007003, uct-cosmology-00/06, AEI-2000-039

Selected References
Last revision: Fri, 18-8-2000 (This page is under construction)