Spacetime Singularities / Gravitational Collapse

  1. Bondi H: The Contraction of Gravitating Spheres, Proc. R. Soc. Lond. A {\bf 281 (1964), 39
    NB: (+ - - -).
  2. Penrose R: Gravitational Collapse and Space-Time Singularities, Phys. Rev. Lett. 14 (1965), 57
    NB: (+ - - -).
  3. Hawking S W: Occurrence of Singularities in Open Universes, Phys. Rev. Lett. 15 (1965), 689
    NB: (+ - - -).
  4. Hawking S W, G F R Ellis: The Cosmic Black-Body Radiation and the Existence of Singularities in our Universe, Astrophys. J. 152 (1968), 25
  5. Belinski\v{\i} V A, I M Khalatnikov, E M Lifshitz: Oscillatory Approach to a Singular Point in the Relativistic Cosmology, Adv. Phys. 19 (1970), 525
  6. Hawking S W and R Penrose: The Singularities of Gravitational Collapse and Cosmology, Proc. R. Soc. Lond. A 314 (1970), 529
    NB: (+ - - -). Communicated by H Bondi.
  7. Khalatnikov I M, E M Lifshitz: General Cosmological Solution of the Gravitational Equations with a Singularity in Time, Phys. Rev. Lett. 24 (1970), 76
  8. Zel'dovich Ya B: Gravitational Instability: An Approximate Theory for Large Scale Density Perturbations, Astron. Astrophys. 5 (1970), 84
  9. 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.
  10. Clarke C J S, B G Schmidt: Singularities: The State of the Art, Gen. Rel. Grav. 8 (1977), 129
  11. Ellis G F R, B G Schmidt: Singular Space-Times (Review Article), Gen. Rel. Grav. 8 (1977), 915
  12. Wheeler J A: Singularity and Unanimity, Gen. Rel. Grav. 8 (1977), 713
  13. Belinski\v{\i} V A, I M Khalatnikov, E M Lifshitz: A General Solution of the Einstein Equations with a Time Singularity, Adv. Phys. 31 (1982), 639
  14. 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.).
  15. Ellis G F R, W L Roque: The Nature of the Initial Singularity, Gen. Rel. Grav. 17 (1985), 397
  16. Madsen M S, D R Matravers: Structure of the Initial Singularity in LRS Bianchi Type-V Models, Class. Quantum Grav. 3 (1986), 541
  17. 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.
  18. 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.
  19. Brauer U, E Malec: Trapped Surfaces Due to Spherical Inhomogeneities in Expanding Open Universes, Class. Quantum Grav. 9 (1992), 905
    NB: Spherically symmetric inhomogeneities on a $k=0$ FLRW geometry.
  20. Joshi P S, I H Dwivedi: Strong Curvature Naked Singularities in Non-Self-Similar Gravitational Collapse, Gen. Rel. Grav. 24 (1992), 129
    NB: Imploding (null) radiation (Vaidya spacetime geometry).
  21. Rácz I, R M Wald: Extensions of Spacetimes with Killing Horizons, Class. Quantum Grav. 9 (1992), 2643
    NB: Quite technical.
  22. Shapiro S L, S A Teukolsky: Gravitational Collapse Of Rotating Spheroids And The Formation Of Naked Singularities, Phys. Rev. D 45 (1992), 2006
  23. Tod K P: The Hoop Conjecture and the Gibbons-Penrose Construction of Trapped Surfaces, Class. Quantum Grav. 9 (1992), 1581
  24. Barrow J D, P Saich: Gravitational Collapse of Rotating Pancakes, Class. Quantum Grav. 10 (1993), 79
    NB: Inclusion of vorticity effects into the Zel'dovich approximation.
  25. Choptuik M W: Universality and Scaling in Gravitational Collapse of a Massless Scalar Field, Phys. Rev. Lett. 70 (1993), 9
  26. Kriele M: Cosmic Censorship in Spherically Symmetric Perfect Fluid Spacetimes, Class. Quantum Grav. 10 (1993), 1525.
    NB: Very technical.
  27. Alfens U, H Müller zum Hagen: Spherically Symmetric Event Horizons and Trapped Surfaces Developing from Innocuous Data, Class. Quantum Grav. 11 (1994), 2705
    NB: Very technical.
  28. Brauer U, A Rendall, O Reula: The Cosmic No-Hair Theorem and the Non-Linear Stability of Homogeneous Newtonian Cosmological Models, Class. Quantum Grav. 11 (1994), 2283. Also: Preprint gr-qc/9403050.
    NB: Newtonian cosmology in terms of Newton-Cartan theory. Perfect fluid plus positive $\Lambda$.
  29. Clarke C J S: A Review of Cosmic Censorship, Class. Quantum Grav. 11 (1994), 1375
  30. Thorne K S: Ch. 13: Inside Black Holes, Black Holes and Time Warps: Einstein's Outrageous Legacy, (New York: Norton & Co., 1994)
  31. Unnikrishnan C S: Naked Singularities in Spherically Symmetric Gravitational Collapse: A Critique, Gen. Rel. Grav. 26 (1994), 655
  32. Joshi P S, T P Singh: Reply to Unnikrishnan on Naked Singularities, Gen. Rel. Grav. 27 (1995), 921
  33. Kasai M: Tetrad-Based Perturbative Approach to Inhomogeneous Universes: A General Relativistic Version of the Zel'dovich Approximation, Phys. Rev. D 52 (1995), 5605
  34. Kriele M, G Lim: Physical Properties of Geometric Singularities, Class. Quantum Grav. 12 (1995), 3019
    NB: Very technical.
  35. Montani G: On the General Behaviour of the Universe Near the Cosmological Singularity, Class. Quantum Grav. 12 (1995), 2505
    NB: Starts off from the BKL scenario.
  36. Rendall A D: Crushing Singularities in Spacetimes with Spherical, Plane and Hyperbolic Symmetry, Class. Quantum Grav. 12 (1995), 1517. Also: Preprint gr-qc/9411011.
  37. Hamadé R S, J M Stewart: The Spherically Symmetric Collapse of a Massless Scalar Field, Class. Quantum Grav. 13 (1996), 497. Also: Preprint gr-qc/9506044.
  38. Joshi P S, A Królak: Naked Strong Curvature Singularities in Szekeres Spacetimes, Class. Quantum Grav. 13 (1996), 3069. Also: Preprint gr-qc/9605033.
  39. Roberts M D: Imploding Scalar Fields, J. Math. Phys. 37 (1996), 4557. Also: Preprint gr-qc/9905006.
  40. K S Virbhadra, S Jhingan, P S Joshi: Nature of Singularity in Einstein-Massless Scalar Theory, Int.J.Mod.Phys. D 6 (1997), 357. Also: Preprint gr-qc/9512030.
  41. 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.
  42. Christodoulou D: On the Global Initial Value Problem and the Issue of Singularities (Review), Class. Quantum Grav. 16 (1999), A23
    NB: Einstein field equations in vacuum (asymptoticaly flat cases) and with massless scalar field.
  43. Rendall A D: Local and Global Existence Theorems for the Einstein Equations, Max-Planck-Gesellschaft Living Reviews Series, No. 2000-1
  44. Ringström H: Curvature Blow Up in Bianchi VIII and IX Spacetimes, Class. Quantum Grav. 17 (2000), 713. Also: Preprint gr-qc/9911115.
    NB: Vacuum case. Employs the dimensionless orthonormal frame formulation of Wainwright and Hsu (1989).

Selected References
Last revision: Tue, 22-8-2000 (This page is under construction)