Isotropic / Conformal Initial Singularities

1. Lifshitz E M, I M Khalatnikov, Investigations in Relativistic Cosmology, Adv. Phys. 12 (1963), 185
   NB: Coins the term "quasi-isotropic singularity".
2. Eardley D, E Liang, R Sachs: Velocity-Dominated Singularities in Irrotational Dust Cosmologies, J. Math. Phys. 13 (1972), 99
   NB: Introduces the notions of "velocity-dominated" and "Friedmann-like" (initial) singularities; employs as examples for analysing the singularity structure the exact solutions for plane symmetric and spherically symmetric expanding dust models (LRS class II); fairly technical.
3. Barrow J D: Quiescent Cosmology, Nature 272 (1978), 211
   NB: Coins the term "isotropic singularity"; (quiescent: at rest, motionless, passive).
4. Penrose R: Singularities and Time-Asymmetry, in General Relativity: An Einstein Centenary Survey, Eds. S W Hawking, W Israel, (Cambridge: Cambridge University Press, 1979), 581
   NB: Establishes the Weyl curvature hypothesis (WCH) for the initial singularity.
5. Goode S W, J Wainwright: Isotropic Singularities in Cosmological Models, Class. Quantum Grav. 2 (1985), 99
   NB: The introductory paper on their continued programme of investigations relating to "isotropic singularities" (cf.: Barrow 1978), "quiescent cosmology" and Penrose's Weyl curvature hypothesis (here: WTH). (- + + +).
6. Goode S W: Vorticity and Isotropic Singularities, Gen. Rel. Grav. 19 (1987), 1075
7. Tod K P: Quasi-Local Mass and Cosmological Singularities, Class. Quantum Grav. 4 (1987), 1457
8. Penrose R: Difficulties with Inflationary Cosmology, in Proc. 14th Texas Symp. on Relativistic Astrophysics, Ed. E J Fergus, (New York: New York Academy of Sciences, 1989) 249
9. Tod K P: Isotropic Singularities and the $\gamma = 2$ Equation of State, Class. Quantum Grav. 7 (1990), L13
10. Goode S W: Isotropic Singularities and the Penrose-Weyl Tensor Hypothesis, Class. Quantum Grav. 8 (1991), L1
11. Tod K P: Isotropic Singularities and the Polytropic Equation of State, Class. Quantum Grav. 8 (1991), L77
12. Goode S W, A A Coley, J Wainwright: The Isotropic Singularity in Cosmology, Class. Quantum Grav. 9 (1992), 445
    NB: Good introduction into the motivation for inflationary scenarios.
13. Newman R P A C: On the Structure of Conformal Singularities in Classical General Relativity, Proc. R. Soc. Lond. A 443 (1993), 473
    NB: Provides arguments why "conformal singularity" should be preferred to "isotropic singularity". (+ - - -).
14. Newman R P A C: On the Structure of Conformal Singularities in Classical General Relativity. II Evolution Equations and a Conjecture of K P Tod, Proc. R. Soc. Lond. A 443 (1993), 493
    NB: Discusses the Cauchy initial value problem for barotropic perfect fluid cosmological models with conformal singularity when $\gamma = 4/3$. (+ - - -).
15. Tod K P: Mach's Principle and Isotropic Singularities, in The Renaissance of General Relativity and Cosmology, Eds. G Ellis, A Lanza, J Miller, (Cambridge: Cambridge University Press, 1993)
16. Claudel C M, K P Newman: The Cauchy Problem for Quasi-Linear Hyperbolic Evolution Problems with a Singularity in the Time, Proc. R. Soc. Lond. A 454 (1998), 1073
    NB: Very technical.
17. Anguige K, K P Tod: Isotropic Cosmological Singularities I. Polytropic Perfect Fluid Spacetimes, Ann. Phys. (N.Y.) 276 (1999), 257. Also: Preprint gr-qc/9903008.
    NB: $p(\mu) = (\gamma-1)\,\mu$, $1 < \gamma \leq 2$. (+ - - -).
18. Anguige K, K P Tod: Isotropic Cosmological Singularities II. The Einstein-Vlasov System, Ann. Phys. (N.Y.) 276 (1999), 294. Also: Preprint gr-qc/9903009.
    NB: Collisionless gas of massless particles, existence of unique solutions proved for spatially homogeneous subcase. (+ - - -).
19. Anguige K: Isotropic Cosmological Singularities III. The Cauchy Problem for the Inhomogeneous Conformal Einstein-Vlasov Equations, Ann. Phys. (N.Y.) 282 (2000), 395. Also: Preprint gr-qc/9903018.
    NB: Collisionless gas of massless particles (i.e., $T^{a}{}_{a} = 0$), existence of unique solutions proved in general spatially inhomogeneous case.

Selected References
Last revision: Wes, 16-8-2000 (This page is under construction)