Spatially Inhomogeneous Cosmological Models

  1. Lema\^{\i}tre G: L'Univers en Expansion, Ann. Soc. Sci. Bruxelles I A 53 (1933), 51 [in French]
    English translation: Gen. Rel. Grav. 29 (1997), 641
  2. Tolman R C: Effect of Inhomogeneity in Cosmological Models, Proc. Nat. Acad. Sci. U.S. 20 (1934), 69
  3. Bondi H: Spherically Symmetric Models in General Relativity, Mon. Not. R. Astron. Soc. 107 (1947), 410
  4. Szekeres P: A Class of Inhomogeneous Cosmological Models, Commun. Math. Phys. 41 (1975), 55
  5. Wainwright J: Characterization of the Szekeres Inhomogeneous Cosmologies as Algebraically Special Spacetimes, J. Math. Phys. 18 (1977), 672
  6. Collins C B, D A Szafron: A New Approach to Inhomogeneous Cosmologies: I.-III., J. Math. Phys. 20 (1979), 2347-2370
  7. MacCallum M A H: Anisotropic and Inhomogeneous Relativistic Cosmologies, in General Relativity: An Einstein Centenary Survey, Eds. S W Hawking, W Israel, (Cambridge: Cambridge University Press, 1979), 533
  8. Wainwright J: A Classification Scheme for Non-Rotating Inhomogeneous Cosmologies, J. Phys. A: Math. Gen. 12 (1979), 2015
    NB: Classification in terms of 3-D Riemannian geometries of the spacelike 3-surface orthogonal to the matter fluid flow (intrinsic geometry of 3-surfaces) and the normal, irrotational timelike congruences (extrinsic geometry of 3-surfaces); results are independent of any field eqs; quite technical.
  9. Wainwright J: Exact Spatially Inhomogeneous Cosmologies, J. Phys. A: Math. Gen. 14 (1981), 1131
    NB: Classification of inhomogeneous models with Abelian $G_{2}$ and irrotational perfect fluid.
  10. Goode S W, J Wainwright: Singularities and Evolution of the Szekeres Cosmological Models, Phys. Rev. D 26 (1982), 3315
    NB: Works out the common dynamic features between the two classes of solutions and investigates their asymptotic behaviour (eg. FLRW etc.).
  11. Collins C B, J Wainwright: Role of Shear in General-Relativistic Cosmological and Stellar Models, Phys. Rev. D 27 (1983), 1209
    NB: For a perfect fluid subject to the EFE it is assumed that i) $\Theta \neq 0$, ii) $\omega = 0$, iii) $\sigma = 0$ and iv) $p=p(\mu)$, $(\mu+p) \neq 0$. It follows that any solution is locally either (a) FLRW ($G_{6}$ case), (b) planar symmetric, tilted SH of Type-V (LRS class II with $K = 0$) or its "temporally homogeneous" counterpart ($G_{4}$ case), or (c) spherically symmetric, spatially inhomogeneous (LRS class II with $K > 0$) ($G_{3}$ case). Cases (b) and (c) have $\dot{u} \neq 0$. Imposing a globally physically reasonable equation of state only seems to leave the FLRW case. This work renders a lot of (later) papers on shearfree perfect fluids uninteresting from a physical point of view.
  12. Goode S W: Spatially Inhomogeneous Cosmologies with Heat Flow, Class. Quantum Grav. 3 (1986), 1247
    NB: Eckart-thermodynamics; $\omega_{[\mu\nu]}=0$; subclass of Szekeres dust solutions (1975); "non-thermalised fluid as source, non-zero spatial temperature gradient".
  13. Futamase T: Approximation Scheme for Constructing a Clumpy Universe in General Relativity, Phys. Rev. Lett. 61 (1988), 2175
  14. Barnes A, R R Rowlingson: Irrotational Perfect Fluids with a Purely Electric Weyl Tensor, Class. Quantum Grav. 6 (1989), 949
  15. Deng Y, P D Mannheim: Shear-free Spherically Symmetric Inhomogeneous Cosmological Model with Heat Flow and Bulk Viscosity, Phys. Rev. D 42 (1990), 371
    NB: First-order Eckart IT only.
  16. Lima J A S, M A S Nobre: Inhomogeneous Two-Fluid Cosmologies With Electromagnetic Field, Class. Quantum Grav. 7 (1990), 399
  17. Bildhauer S, T Futamase: The Age Problem in Inhomogeneous Universes, Gen. Rel. Grav. 23 (1991), 1251
    NB: Very good!!! Problem well exposed, transparent explanation of proposed solution Ansatz. Modifies the Friedmann equation by taking backreactions of inhomogeneities on the expansion rate into account. Sub-Hubble radius scale inhomogeneities are modelled in Newtonian terms and a Zel'dovich approximation to first order is applied. The spatial curvature is assumed to average to zero, $k=0$.
  18. Tomimura N, et al: Inhomogeneous Viscous Cosmologies without Singularity, Class. Quantum Grav. 8 (1991), 969
  19. Calzetta E, M Sakellariadon: Inflation In Inhomogeneous Cosmology, Phys. Rev. D 45 (1992), 2802
  20. Ruiz E, J M M Senovilla: General Class of Inhomogeneous Perfect-Fluid Solutions, Phys. Rev. D 45 (1992), 1995
  21. Kasai M: Inhomogeneous Cosmological Models which are Homogeneous and Isotropic on Average, Phys. Rev. D 47 (1993), 3214
    NB: Irrotational dust in comoving description. Applies spatial averaging (of the energy density, etc) in terms of the physical 3-metric on the 3-surfaces of (synchronous) constant time. Discusses a one-dimensional collapse sub-solution of the Szekeres class as an example of a relativistic version of the Zel'dovich approximation in Newtonian cosmology.
  22. Krisch J P, L L Smalley: Two Fluid Acoustic Modes and Inhomogeneous Cosmologies, Class. Quantum Grav. 10 (1993), 2615
  23. MacCallum M A H: Anisotropic and Inhomogeneous Cosmologies, in The Renaissance of General Relativity and Cosmology, Eds. G Ellis, A Lanza, J Miller, (Cambridge: Cambridge University Press, 1993). Also: Preprint gr-qc/9212014.
  24. Croudace K M, J Parry, D S Salopek, J M Stewart: Applying the Zel'dovich Approximation to General Relativity, Astrophys. J. 423 (1994), 22
  25. Senovilla J M M, C F Sopuerta: New $G_{1}$ and $G_{2}$ Inhomogeneous Cosmological Models from the Generalised Kerr-Schild Transformation, Class. Quantum Grav. 11 (1994), 2073
    NB: $\omega^{a} = 0$, Petrov type D.
  26. Hellaby C: The Null and KS Limits of the Szekeres Model, Class. Quantum Grav. 13 (1996), 2537
  27. Comer G L: 3+1 Approach to the Long-Wavelength Iteration Scheme, Class. Quantum Grav. 14 (1997), 407
    NB: Iteration of large-scale inhomogeneities and anisotropies.
  28. van Elst H, C Uggla, W M Lesame, G F R Ellis, R Maartens: Integrability of Irrotational Silent Cosmological Models, Class. Quantum Grav. 14 (1997), 1151. Also: Preprint gr-qc/9611002.
  29. Wainwright J, G F R Ellis (Eds.): Dynamical Systems in Cosmology, (Cambridge: Cambridge University Press, 1997)
  30. Ellis G F R, H van Elst: Cosmological Models, Cargèse Lectures 1998, in Theoretical and Observational Cosmology, Ed. M Lachièze-Rey, (Dordrecht: Kluwer, 1999), 1. Also: Preprint gr-qc/9812046.
  31. Ellis G F R: 83 Years of General Relativity and Cosmology: Progress and Problems (Review), Class. Quantum Grav. 16 (1999), A37
  32. Mena F C, R Tavakol: Evolution of the Density Contrast in Inhomogeneous Dust Models, Class. Quantum Grav. 16 (1999), 435. Also: Preprint gr-qc/9811035.
  33. Mustapha N, C Hellaby: Clumps into Voids, Preprint astro-ph/0006083
    NB: LTB.

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