SPACETIME SINGULARITIES and Gravitational Collapse: useful references
Two useful sets of references (the second of which is chronological) :
Spacetime Singularities and Gravitational Collapse
(1) Review: Theodore Frankel, Gravitational curvature, an introduction to Einstein's theory, and Hans Stephani, General relativity, an introduction to the theory of the gravitational field, and Robert M. Wald, General relativity
Andrzej Trautman
Source: Bull. Amer. Math. Soc. (N.S.) Volume 14, Number 1 (1986), 152-158.
Reviewed Works:
Theodore Frankel, Gravitational curvature, an introduction to Einstein's theory. W. H. Freeman and Co., San Francisco, California, 1979, xviii + 172 pp., $8.95. ISBN 0-7167-1062-5
Hans Stephani, General relativity, an introduction to the theory of the gravitational field. (edited by John Stewart; translated from German by Martin Pollock and John Stewart) Cambridge Univ. Press, New York, New York, 1982, xvi + 298 pp., $49.50. ISBN 0-521-24008-5
Robert M. Wald, General relativity. University of Chicago Press, Chicago, Illinois, 1984, xiii + 491 pp., $50.00 HB; $30.00 PB. ISBN 0-266-87033-2
Full-text: Access granted (open access)
References
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2. H. Bondi, F. A. E. Pirani and I. Robinson, Gravitational waves in general relativity III. Exact plane waves, Proc. Roy. Soc. London A251 (1959), 519-533.
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Mathematical Reviews (MathSciNet): MR106747
3. E. Cartan, Sur les espaces conformes généralisés et l'Univers optique, C. R. Acad. Sci. Paris 174 (1922), 857-859.
Jahrbuch database (Zbl): 48.0854.04
4. E. Cartan, Sur les variétés à connexion affine et la théorie de la relativité généralisée I; I (suite); II, Ann. Sci. École Norm. Sup. 40 (1923), 325-412; 41 (1924), 1-25; 42 (1925), 17-88. English translation by A. Ashtekar and A. Magnon-Ashtekar, Bibliopolis, Naples, 1985.
Jahrbuch database (Zbl): 51.0582.01
5. S. Chandrasekhar, The mathematical theory of black holes, Clarendon Press, Oxford, 1983.
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Mathematical Reviews (MathSciNet): MR700826
6. S. S. Chern and J. K. Moser, Real hypersurfaces in complex manifolds, Acta Math. 133 (1974), 219-271.
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7. W. K. Clifford, The common sense of the exact sciences, D. Appleton and Co., New York, 1885.
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8. S. Deser and B. Zumino, Consistent supergravity, Phys. Lett. 62B (1976), 335-337.
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9. S. K. Donaldson, Self-dual connections and the topology of smooth 4-manifolds, Bull. Amer. Math. Soc. (N.S.) 8 (1983), 81-83.
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10. A. Einstein and N. Rosen, On gravitational waves, J. Franklin Inst. 223 (1937), 43-54.
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11. D. Z. Freedman, P. Van Nieuwenhuizen and S. Ferrara, Progress toward a theory of supergravity, Phys. Rev. D13 (1976), 3214-18.
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12. A. Friedmann, Über die Krümmung des Raumes, Z. Phys. 10 (1922), 377-386.
13. R. P. Geroch, What is a singularity in general relativity?, Ann. Physics 48 (1968), 526-540.
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14. K. Gödel, An example of a new type of cosmological solutions of Einstein's field equations of gravitation, Rev. Modern Phys. 21 (1949), 447-450.
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15. J. N. Goldberg and R. K. Sachs, A theorem on Petrov types, Acta Phys. Polon. 22 Suppl. (1962), 13-23.
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Mathematical Reviews (MathSciNet): MR156679
16. A. Haefliger, Structures feuilletées et cohomologie à valeur dans un faisceau de groupoïdes, Comment. Math. Helv. 32 (1958), 248-329.
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17. S. W. Hawking and G. F. R. Ellis, The large scale structure of space-time, Cambridge Univ. Press, Cambridge, 1973.
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Mathematical Reviews (MathSciNet): MR424186
18. S. W. Hawking and R. Penrose, The singularities of gravitational collapse and cosmology, Proc. Roy. Soc. London A314 (1970), 529-548.
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19. R. P. Kerr and A. Schild, A new class of vacuum solutions of the Einstein field equations, Atti del Convegno sulla Relatività Generale: Probleme dell'energia e onde gravitazionali, G. Barbèra, Editore, Florence, 1965.
20. T. W. B. Kibble, Lorentz invariance and the gravitational field, J. Math. Phys. 2 (1961), 212-221.
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21. D. Kramer, H. Stephani, M. MacCallum and E. Herlt, Exact solutions of Einstein's field equations, Cambridge Univ. Press and Deutsch Verlag der Wissenschaften, Cambridge and Berlin, 1980.
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22. H. Lewy, An example of a smooth linear partial differential equation without solution, Ann. of Math. (2) 66 (1957), 155-158.
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23. A. Lichnerowicz, Théories relativistes de la gravitation et de l'électromagnétisme, Masson et Cie, Paris, 1955.
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Mathematical Reviews (MathSciNet): MR71917
24. C. W. Misner, K. S. Thorne and J. A. Wheeler, Gravitation, W. H. Freeman and Co., San Francisco, 1973.
Mathematical Reviews (MathSciNet): MR418833
25. E. T. Newman and R. Penrose, An approach to gravitational radiation by a method of spin coefficients, J. Math. Phys. 3 (1962), 566-578; Errata: Ibid. 4 (1963), 998.
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Mathematical Reviews (MathSciNet): MR141500
26. S. P. Novikov, Topology of foliations, Trudy Moskov. Mat. Obšč 14 (1965), 248-278 = Trans. Moscow Math. Soc. (1965), 268-304.
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27. I. Ozsvàth and E. Schücking, The finite rotating universe, Ann. Physics 55 (1969), 166-204.
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28. R. Penrose, Gravitational collapse and space-time singularities, Phys. Rev. Lett. 14 (1965), 57-59.
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29. R. Penrose, Twistor algebra, J. Math. Phys. 8 (1967), 345-366.
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30. R. Penrose, Techniques of differential topology in relativity, SIAM, Philadelphia, 1972.
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31. R. Penrose, Physical space-time and nonrealizable CR-structures, Bull. Amer. Math. Soc. (N.S.) 8 (1983), 427-448.
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Mathematical Reviews (MathSciNet): MR693958
32. R. Penrose and M. A. H. MacCallum, Twistor theory: An approach to the quantisation of fields and space-time, Phys. Rep. 6 (1972), 241-316.
Mathematical Reviews (MathSciNet): MR475660
33. R. Penrose and W. Rindler, Spinors and space-time, Cambridge Univ. Press, Cambridge, vol. I: 1984, vol. II: to appear.
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Mathematical Reviews (MathSciNet): MR776784
34. I. Robinson, Null electromagnetic fields, J. Math. Phys. 2 (1961), 290-291.
Mathematical Reviews (MathSciNet): MR127369
35. I. Robinson and A. Trautman, Integrable optical geometry, Lett. Math. Phys. 10 (1985), 179-182.
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36. I. Robinson and A. Trautman, A generalization of Mariot 's theorem on congruences of null geodesics, Proc. Roy. Soc. London (to appear).
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37. D. W. Sciama, On the analogy between charge and spin in general relativity, Recent developments in General Relativity, Pergamon Press and PWN, Oxford and Warsaw, 1962.
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38. A. H. Taub, Empty space-times admitting a three-parameter group of motions, Ann. of Math. 53 (1951), 472-490.
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39. A. Trautman, Deformations of the Hodge map and optical geometry, J. Geometry and Physics (Florence) 1 (1984), 85-95.
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40. S. Weinberg, Gravitation and cosmology, J. Wiley, New York, 1972.
41. R. O. Wells, Jr., The Cauchy-Riemann equations and differential geometry, Bull. Amer. Math. Soc. (N.S.) 6 (1982), 187-199.
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42. C. N. Yang and R. L. Mills, Conservation of isotopic spin and isotopic gauge invariance, Phys. Rev. 96 (1954), 191-195.
Mathematical Reviews (MathSciNet): MR65437
(2) University of London, Queen Mary College, School of Mathematical Sciences
Spacetime Singularities / Gravitational Collapse / Critical Phenomena
1. Oppenheimer J R, H Snyder: On Continued Gravitational Contraction, Phys. Rev. 56 (1939), 455-459
2. Raychaudhuri A: Relativistic Cosmology. I, Phys. Rev. 98 (1955), 1123-1126.
Reprinted: Gen. Rel. Grav. 32 (2000), 749-756 (GRG "Golden Oldie").
3. Lifshitz E M, I M Khalatnikov: Investigations in Relativistic Cosmology, Adv. Phys. 12 (1963), 185-249
4. Bondi H: The Contraction of Gravitating Spheres, Proc. R. Soc. Lond. A 281 (1964), 39-48
NB: (+ - - -).
5. Misner C W, D H Sharp: Relativistic Equations for Adiabatic, Spherically Symmetric Gravitational Collapse, Phys. Rev. 136 (1964), B571-B576
NB: Matter-comoving gauge, (- + + +).
6. Penrose R: Gravitational Collapse and Space-Time Singularities, Phys. Rev. Lett. 14 (1965), 57-59
NB: (+ - - -).
7. Hawking S W: Occurrence of Singularities in Open Universes, Phys. Rev. Lett. 15 (1965), 689-690
NB: (+ - - -).
8. Hawking S W, G F R Ellis: The Cosmic Black-Body Radiation and the Existence of Singularities in our Universe, Astrophys. J. 152 (1968), 25-36
9. Hawking S, R Penrose: On Gravitational Collapse and Cosmology, 1968.
NB: 2nd Prize Essay of the 1968 Gravity Research Foundation Award.
10. Misner C W: Mixmaster Universe, Phys. Rev. Lett. 22 (1969), 1071-1074
11. Penrose R: Gravitational Collapse: The Role of General Relativity, Rivista del Nuovo Cimento (Numero Speziale) I (1969), 257-276
Reprinted: Gen. Rel. Grav. 34 (2002), 1141-1165 (GRG "Golden Oldie"). NB: Excellent! (+ - - -).
12. Belinskii V A, I M Khalatnikov, E M Lifshitz: Oscillatory Approach to a Singular Point in the Relativistic Cosmology, Adv. Phys. 19 (1970), 525-573
NB:: Synchronous temporal gauge.
13. Hawking S W and R Penrose: The Singularities of Gravitational Collapse and Cosmology, Proc. R. Soc. Lond. A 314 (1970), 529-548
NB: (+ - - -). Communicated by H Bondi.
14. Khalatnikov I M, E M Lifshitz: General Cosmological Solution of the Gravitational Equations with a Singularity in Time, Phys. Rev. Lett. 24 (1970), 76-79
15. Zel'dovich Ya B: Gravitational Instability: An Approximate Theory for Large Scale Density Perturbations, Astron. Astrophys. 5 (1970), 84-
16. Eardley D, E Liang, R Sachs: Velocity-Dominated Singularities in Irrotational Dust Cosmologies, J. Math. Phys. 13 (1972), 99-107
NB: Matter-comoving formulation. 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.
17. Szekeres P: Quasispherical gravitational collapse, Phys. Rev. D 12 (1975), 2941-2948
18. Clarke C J S, B G Schmidt: Singularities: The State of the Art, Gen. Rel. Grav. 8 (1977), 129-137
19. Ellis G F R, B G Schmidt: Singular Space-Times (Review Article), Gen. Rel. Grav. 8 (1977), 915-953
20. Wheeler J A: Singularity and Unanimity, Gen. Rel. Grav. 8 (1977), 713-715
21. Eardley D M, L Smarr: Time Functions in Numerical Relativity: Marginally Bound Dust Collapse, Phys. Rev. D 19 (1979), 2239-2259
NB: Lemaître-Tolman-Bondi dust models investigated; introduces definition of class of "crushing singularities".
22. Belinskii V A, I M Khalatnikov, E M Lifshitz: A General Solution of the Einstein Equations with a Time Singularity, Adv. Phys. 31 (1982), 639-667
23. Goode S W, J Wainwright: Singularities and Evolution of the Szekeres Cosmological Models, Phys. Rev. D 26 (1982), 3315-3326
NB: Simultaneous synchronous and matter-comoving temporal gauges; works out the common dynamic features between the two classes of solutions and investigates their asymptotic behaviour (eg. FLRW etc.); for models with positive energy density all initial and final singularities are Kasner-like (convergent).
24. Wainwright J: Power Law Singularities in Orthogonal Spatially Homogeneous Cosmologies, Gen. Rel. Grav. 16 (1984), 657-674
25. Ellis G F R, W L Roque: The Nature of the Initial Singularity, Gen. Rel. Grav. 17 (1985), 397-406
26. Collins C B, J M Lang: Singularities in Self-Similar Spacetimes, Class. Quantum Grav. 3 (1986), 1143-1150
27. Madsen M S, D R Matravers: Structure of the Initial Singularity in LRS Bianchi Type-V Models, Class. Quantum Grav. 3 (1986), 541-546
28. Newman R P A C: Strengths of Naked Singularities in Tolman-Bondi Spacetimes, Class. Quantum Grav. 3 (1986), 527-539
29. Ori A, T Piran: Naked Singularities in Self-Similar Spherical Gravitational Collapse, Phys. Rev. Lett. 59 (1987), 2137-2140
30. Roberts M D: Scalar Field Counterexamples to the Cosmic Censorship Hypothesis, Gen. Rel. Grav. 21 (1989), 907-939
31. Isenberg J, V Moncrief: Asymptotic Behavior of the Gravitational Fields and the Nature of Singularities in Gowdy Spacetimes, Ann. Phys. (N.Y.) 199 (1990), 84-122
NB: Polarised Gowdy case only; establishes concept of "asymptotically velocity term dominated" singularities; employs method of "energy functionals" to prove existence theorems.
32. Ori A, T Piran: Naked Singularities and other Features of Self-Similar General-Relativistic Gravitational Collapse, Phys. Rev. D 42 (1990), 1068-1090
NB: (- + + +); (Eulerian) Schwarzschild-like time slicing and matter-comoving approaches. Employing Runge-Kutta numerical integration schemes, investigates spherically symmetrical perfect fluid collapse models with equation of state $p = k\,\rho$ that are locally determined by a density and a velocity parameter. "Asymptotically quasi-static solutions" according to Carr et al, Class. Quantum Grav. 18 (2001), 303. Discovers the "band structure" of solutions that are regular (analytic) at the centre and on the sonic surface. Also investigates the behaviour of in-/out-going null geodesics. Reviews the Newtonian self-similar solutions of Penston and Larson. There exist analytic general-relativistic generalisations of the Penston-Larson solutions for $0 < k < 0.036$.
33. Senovilla J M M: New Class of Inhomogeneous Cosmological Perfect-Fluid Solutions without Big-Bang Singularity, Phys. Rev. Lett. 64 (1990), 2219-2221
NB: Matter-comoving temporal gauge. Diagonal line element (both KVF HSO: polarised) with separable metric functions; conformal lapse function. 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 only one constant essential parameter $a$. $\mathbb{R}^{3}$ spatial topology; change to cylindrically symmetrical $\mathbb{R}^{2}\times\mathbb{S}^{1}$ spatial topology discussed.
34. Brauer U, E Malec: Trapped Surfaces Due to Spherical Inhomogeneities in Expanding Open Universes, Class. Quantum Grav. 9 (1992), 905-920
NB: Spherically symmetric inhomogeneities on a $k=0$ FLRW geometry.
35. Joshi P S, I H Dwivedi: Strong Curvature Naked Singularities in Non-Self-Similar Gravitational Collapse, Gen. Rel. Grav. 24 (1992), 129-137
NB: Imploding (null) radiation (Vaidya spacetime geometry).
36. Rácz I, R M Wald: Extensions of Spacetimes with Killing Horizons, Class. Quantum Grav. 9 (1992), 2643-2656
NB: Quite technical.
37. Shapiro S L, S A Teukolsky: Gravitational Collapse Of Rotating Spheroids And The Formation Of Naked Singularities, Phys. Rev. D 45 (1992), 2006-2012
38. Tod K P: The Hoop Conjecture and the Gibbons-Penrose Construction of Trapped Surfaces, Class. Quantum Grav. 9 (1992), 1581-1591
39. Barrow J D, P Saich: Gravitational Collapse of Rotating Pancakes, Class. Quantum Grav. 10 (1993), 79-91
NB: Inclusion of vorticity effects into the Zel'dovich approximation.
40. Berger B K, V Moncrief: Numerical Investigation of Cosmological Singularities, Phys. Rev. D 48 (1993), 4676-4687. Also: Preprint arXiv:gr-qc/9307032v1.
NB: Investigation conducted within family of Gowdy vacuum spacetimes with spatial topology $T^{3}$; first detection of development of small scale spiky spatial structure in approach to initial singularity.
41. Choptuik M W: Universality and Scaling in Gravitational Collapse of a Massless Scalar Field, Phys. Rev. Lett. 70 (1993), 9-12
42. Kriele M: Cosmic Censorship in Spherically Symmetric Perfect Fluid Spacetimes, Class. Quantum Grav. 10 (1993), 1525-1539.
NB: Very technical. (Dept of Pure Maths, U of Waterloo).
43. Alfens U, H Müller zum Hagen: Spherically Symmetric Event Horizons and Trapped Surfaces Developing from Innocuous Data, Class. Quantum Grav. 11 (1994), 2705-2721
NB: Very technical. (U der Bundeswehr, Maschinenbau).
44. 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), 2283-2296. Also: Preprint gr-qc/9403050.
NB: Newtonian cosmology in terms of Newton-Cartan theory. Perfect fluid plus positive $\Lambda$.
45. Clarke C J S: A Review of Cosmic Censorship (Review Article), Class. Quantum Grav. 11 (1994), 1375-1386
46. Evans C R, J S Coleman: Critical Phenomena and Self-Similarity in the Gravitational Collapse of Radiation Fluid, Phys. Rev. Lett. 72 (1994), 1782-1785. Also: Preprint gr-qc/9402041.
NB: (- + + +); (Eulerian) Schwarzschild-like time slicing approach. Numerical investigations of full Einstein field equations for spherically symmetrical collapse of radiation fluid. Observes asymptotic approach of near-critical configurations to a self-similar solution near centre of collapse. Cauchy data: energy density profile, radial fluid velocity.
47. Matarrese S, O Pantano, D Saez: General Relativistic Dynamics of Irrotational Dust: Cosmological Implications, Phys. Rev. Lett. 72 (1994), 320-323. Also: Preprint astro-ph/9310036.
48. Thorne K S: Ch. 13: Inside Black Holes, Black Holes and Time Warps: Einstein's Outrageous Legacy, (New York: Norton & Co., 1994)
49. Unnikrishnan C S: Naked Singularities in Spherically Symmetric Gravitational Collapse: A Critique, Gen. Rel. Grav. 26 (1994), 655-662
50. Joshi P S, T P Singh: Reply to Unnikrishnan on Naked Singularities, Gen. Rel. Grav. 27 (1995), 921-932
51. Kasai M: Tetrad-Based Perturbative Approach to Inhomogeneous Universes: A General Relativistic Version of the Zel'dovich Approximation, Phys. Rev. D 52 (1995), 5605-5611
52. Kriele M, G Lim: Physical Properties of Geometric Singularities, Class. Quantum Grav. 12 (1995), 3019-3035
NB: Very technical. (TU Berlin, Mathematik).
53. Montani G: On the General Behaviour of the Universe Near the Cosmological Singularity, Class. Quantum Grav. 12 (1995), 2505-2517
NB: Starts off from the BKL scenario.
54. Rendall A D: Crushing Singularities in Spacetimes with Spherical, Plane and Hyperbolic Symmetry, Class. Quantum Grav. 12 (1995), 1517-1533. Also: Preprint gr-qc/9411011.
55. Hamadé R S, J M Stewart: The Spherically Symmetric Collapse of a Massless Scalar Field, Class. Quantum Grav. 13 (1996), 497-512. Also: Preprint gr-qc/9506044.
56. Joshi P S, A Królak: Naked Strong Curvature Singularities in Szekeres Spacetimes, Class. Quantum Grav. 13 (1996), 3069-3074. Also: Preprint gr-qc/9605033.
57. Roberts M D: Imploding Scalar Fields, J. Math. Phys. 37 (1996), 4557-4573. Also: Preprint gr-qc/9905006.
58. Virbhadra K S, S Jhingan, P S Joshi: Nature of Singularity in Einstein-Massless Scalar Theory, Int. J. Mod. Phys. D 6 (1997), 357-362. Also: Preprint gr-qc/9512030.
59. Foster S: Scalar Field Cosmologies and the Initial Spacetime Singularity, Class. Quantum Grav. 15 (1998), 3485-3504. Also: Preprint gr-qc/9806098.
NB: Treats scalar fields with arbitrary non-negative potential in spatially flat FL models, using a dynamical systems approach.
60. Kichenassamy S, A D Rendall: Analytic Description of Singularities in Gowdy Spacetimes, Class. Quantum Grav. 15 (1998), 1339-1355
NB: Transforms EFE to a system of Fuchsian PDE for constructing singular solutions.
61. Rein G, A D Rendall, J Schaeffer: Critical Collapse of Collisionless Matter: A Numerical Investigation, Phys. Rev. D 58 (1998), 044007. Also: Preprint gr-qc/9804040.
NB: (Eulerian) Schwarzschild-like time slicing approach.
62. Christodoulou D: On the Global Initial Value Problem and the Issue of Singularities (Review), Class. Quantum Grav. 16 (1999), A23-A35
NB: Einstein field equations in vacuum (asymptoticaly flat cases) and with massless scalar field.
63. Gundlach C: Critical Phenomena in Gravitational Collapse, Max-Planck-Gesellschaft Living Reviews Series, No. 1999-4
64. Carr B J, A A Coley, M Goliath, U S Nilsson, C Uggla: Critical Phenomena and a New Class of Self-Similar Spherically Symmetric Perfect-Fluid Solutions, Phys. Rev. D 61 (2000), 081502 (1-5). Also: Preprint gr-qc/9901031.
NB: Matter-comoving and homothetic approaches. Equation of state: $p = alpha\,\mu$. Critical solution belongs for i) $0 < \alpha \leq 0.28$ to "asymptotically quasi-static models", ii) $\alpha \approx 0.28$ to "asymptotically Minkowski models of class B", iii) $0.28 \leq \alpha < 1$ to "asymptotically Minkowski models of class A".
65. Mena F C, R Tavakol, P S Joshi: Initial Data and Spherical Dust Collapse, Phys. Rev. D 62 (2000), 044001. Also: Preprint gr-qc/0002062.
66. Neilsen D W, M W Choptuik: Ultrarelativistic fluid dynamics, Class. Quantum Grav. 17 (2000), 733-759. Also: Preprint gr-qc/9904052.
NB: (Eulerian) Schwarzschild-like time slicing approach. Critical collapse of spherically symmetric perfect fluids with equation of state $p = (\gamma-1)\,\rho$, $1.9 \leq \gamma \leq 2$. Numerical integration of both the full Einstein field equations (using a high-resolution shock-capturing scheme according to LeVeque) and the self-similar Einstein field equations (using the MAPLE V LSODE solver).
67. Neilsen D W, M W Choptuik: Critical phenomena in perfect fluids, Class. Quantum Grav. 17 (2000), 761-782. Also: Preprint gr-qc/9812053.
NB: (Eulerian) Schwarzschild-like time slicing approach. Critical collapse of spherically symmetric perfect fluids with equation of state $p = (\gamma-1)\,\rho$, $1.9 \leq \gamma \leq 2$. Numerical integration of both the full Einstein field equations (using a high-resolution shock-capturing scheme according to LeVeque) and the self-similar Einstein field equations (using the MAPLE V LSODE solver).
68. Rendall A D: Fuchsian Analysis of Singularities in Gowdy Spacetimes beyond Analyticity, Class. Quantum Grav. 17 (2000), 3305-3316. Also: Preprint gr-qc/0004044.
69. Ringström H: Curvature Blow Up in Bianchi VIII and IX Vacuum Spacetimes, Class. Quantum Grav. 17 (2000), 713-731. Also: Preprint gr-qc/9911115.
NB: Vacuum case. Employs the dimensionless orthonormal frame formulation of Wainwright and Hsu (1989).
70. Andersson L, A D Rendall: Quiescent Cosmological Singularities, Commun. Math. Phys. 218 (2001), 479-511. Also: Preprint gr-qc/0001047.
NB: Fuchsian algorithm for non-oscillatory past asymptotic dynamics applied to the case of G0 cosmologies with massless scalar field matter source.
71. Ringström H: The Bianchi IX Attractor, Ann. H. Poincaré 2 (2001), 405-500. Also: Preprint gr-qc/9911115.
NB: Orthogonal perfect fluid with linear equation of state and zero cosmological constant. Employs the dimensionless orthonormal frame formulation of Wainwright and Hsu (1989).
72. Harada T, H Maeda: Convergence to a Self-Similar Solution in General Relativistic Gravitational Collapse, Phys. Rev. D 63 (2001), 084022 (1-14). Also: Preprint gr-qc/0101064.
NB: Matter-comoving approach. Using staggered leapfrog scheme, 10000 spatial grid points and time-symetrical initial data, numerically integrates full spherically symmetrical Einstein field equations for perfect fluids with equation of state $p = k\,\rho$ in Misner-Sharp form. Provides numerical evidence that for $0 < k \leq 0.036$ (extremely soft equation of state) the generic collapse solution approaches the self-similar general relativistic Penston-Larson state. These contain naked singularities.
73. Nolan B C: Sectors of Spherical Homothetic Collapse, Class. Quantum Grav. 18 (2001), 1651-1675. Also: Preprint gr-qc/0010032.
74. Berger B K: Numerical Approaches to Spacetime Singularities, Max-Planck-Gesellschaft Living Reviews Series, No. 2002-1.
NB: First update of original article.
75. Brady, P R, M W Choptuik, C Gundlach, D W Neilsen: Black-Hole Threshold Solutions in Stiff Fluid Collaose, Class. Quantum Grav. 19 (2002), 6359-6375. Also: Preprint gr-qc/0207096.
76. van Elst H, C Uggla, J Wainwright: Dynamical Systems Approach to G2 Cosmology, Class. Quantum Grav. 19 (2002), 51-82. Also: Preprint gr-qc/0107041.
77. Garfinkle D: Harmonic Coordinate Method for Simulating Generic Singularities, Phys. Rev. D 65 (2002), 044029 (1-6). Also: Preprint gr-qc/0110013.
78. Uggla C, H van Elst, J Wainwright, G F R Ellis: The Past Attractor in Inhomogeneous Cosmology, Phys. Rev. D 68 (2003), 103502 (1-22). Also: Preprint gr-qc/0304002.
NB: "Paper I".
79. Garfinkle D: Numerical Simulations of Generic Singularities, Phys. Rev. Lett. 93 (2004), 161101 (1-4). Also: Preprint gr-qc/0312117.
NB: Employs scale-invariant formalism of Uggla et al. 2003 in separable volume temporal gauge. [Fermi-propagated spatial frame.]
80. Harada T: Gravitational Collapse and Naked Singularities, Preprint gr-qc/0407109.
81. Lim W C: The Dynamics of Inhomogeneous Cosmologies, Ph.D. thesis, University of Waterloo (Canada), Preprint gr-qc/0410126
NB: Advisor: John Wainwright.
82. Andersson L, H van Elst, W C Lim, C Uggla: Asymptotic Silence of Generic Cosmological Singularities, Phys. Rev. Lett. 94 (2005), 051101 (1-4). Also: Preprint gr-qc/0402051.
83. Coley A A, W C Lim: Asymptotic Analysis of Spatially Inhomogeneous Stiff and Ultra-Stiff Cosmologies, Class. Quantum Grav. 22 (2005), 3073-3082. Also: Preprint gr-qc/0506097.
NB: Gives decay rates into the past for Hubble-normalised orthonormal frame variables in stiff perfect fluid G0 cosmologies; separable volume temporal gauge.
84. Curtis J, D Garfinkle: Numerical Simulations of Stiff Fluid Gravitational Singularities, Phys. Rev. D 72 (2005), 064003 (1-7). Also: Preprint gr-qc/0506107.
NB: Employs scale-invariant formalism of Uggla et al. 2003 in separable volume temporal gauge. [Fermi-propagated spatial frame.]
85. Rendall A D: The Nature of Spacetime Singularities, Preprint gr-qc/0503112.
86. Rendall A D: Theorems on Existence and Global Dynamics for the Einstein Equations, Max-Planck-Gesellschaft Living Reviews Series, No. 2005-6.
NB: Third update of original article.
87. Dafermos M, A D Rendall: Strong Cosmic Censorship for T2-Symmetric Cosmological Spacetimes with Collisionless Matter, Preprint gr-qc/0610075
88. Lim W C, C Uggla, J Wainwright: Asymptotic Silence-Breaking Singularities, Class. Quantum Grav. 23 (2006), 2607-2630. Also: Preprint gr-qc/0511139.
89. Uggla C: Spacetime Singularities (Einstein-Online)
90. Beyer F: Asymptotics and Singularities in Cosmological Models with Positive Cosmological Constant, Ph.D. thesis, Albert-Einstein Institut, Golm and University of Potsdam, 2007, Preprint arXiv:0710.4297v1 [gr-qc]
NB: Advisor: Helmut Friedrich.
91. Garfinkle D: Numerical Simulations of General Gravitational Singularities, Class. Quantum Grav. 24 (2007), S295-S306
92. Heinzle J M, C Uggla, N Röhr: The Cosmological Billard Attractor, Preprint gr-qc/0702141
93. Joshi P S: On the Genericity of Spacetime Singularities, Preprint gr-qc/0702116
94. Lim W C: New Explicit Spike Solution - Non-Local Component of the Billiard Attractor, Preprint arXiv:0710.0628v1 [gr-qc]
95. Lim W C, A A Coley, S Hervik: Kinematic and Weyl singularities, Class. Quantum Grav. 24 (2007), 595-604. Also: Preprint gr-qc/0608134.
NB: Discusses nature of future singularities in tilted SH models of irrotational Type-V, Type-VII0, Type-VIIh, and LRS Type-V.
96. Montani G, M V Battisti, R Benini, G Imponente: Classical and Quantum Features of the Mixmaster Singularity, Preprint arXiv:0712.3008v1 [gr-qc]
97. Uggla C: The Nature of Generic Cosmological Singularities, Preprint arXiv:0706.0463v1 [gr-qc]
NB: Invited talk at the 11th Marcel Grossmann Meeting on Recent Developments in General Relativity, Berlin, Germany, 23-29 July 2006.
98. Damour T, S de Buyl: Describing General Cosmological Singularities in Iwasawa Variables, Phys. Rev. D 77 (2008), 043520 (1-26). Also: Preprint arXiv:0710.5692v1 [gr-qc].
99. Lim W C: New Explicit Spike Solutions - Non-Local Component of the Generalized Mixmaster Attractor, Class. Quantum Grav. 25 (2008), 045014 (1-17). Also: Preprint arXiv:0710.0628v2 [gr-qc].
NB: Generates spike solutions within the family of Gowdy vacuum spacetimes by successively employing the rotation and Gowdy-to-Ernst transformations of Rendall and Weaver, Class. Quantum Grav. 18 (2001), 2959-2975, to Taub's vacuum solutions of Bianchi Type-II.
