![]() |
1 | Abrahams, A.M., and Evans, C.R., “Critical behavior and scaling in vacuum axisymmetric
gravitational collapse”, Phys. Rev. Lett., 70, 2980–2983, (1993). [![]() |
![]() |
2 | Abrahams, A.M., and Evans, C.R., “Universality in axisymmetric vacuum collapse”, Phys. Rev.
D, 49, 3998–4003, (1994). [![]() |
![]() |
3 | Aichelburg, P.C., Bizoń, P., and Tabor, Z., “Bifurcation and fine structure phenomena in
critical collapse of a self-gravitating σ-field”, Class. Quantum Grav., 23, S299–S306, (2006).
[![]() ![]() |
![]() |
4 | Alcubierre, M., Allen, G., Brügmann, B., Lanfermann, G., Seidel, E., Suen, W.-M., and Tobias,
M., “Gravitational collapse of gravitational waves in 3D numerical relativity”, Phys. Rev. D,
61, 041501, 1–5, (2000). [![]() ![]() |
![]() |
5 | Álvarez-Gaumé, L., Gómez, C., and Vázquez-Mozo, M.A., “Scaling Phenomena in Gravity
from QCD”, Phys. Lett. B, 649, 478–482, (2007). [![]() ![]() |
![]() |
6 | Álvarez-Gaumé, L., Gómez, C., Vera, A.S., Tavanfar, A., and Vázquez-Mozo, M.A.,
“Critical formation of trapped surfaces in the collision of gravitational shock waves”, J. High
Energy Phys.(02), 009, (2009). [![]() ![]() |
![]() |
7 | Álvarez-Gaumé, L., Gómez, C., Vera, A.S., Tavanfar, A., and Vázquez-Mozo, M.A.,
“Critical gravitational collapse: Towards a holographic understanding of the Regge region”,
Nucl. Phys. B, 806, 327–385, (2009). [![]() ![]() |
![]() |
8 | Andreasson, H., and Rein, G., “A numerical investigation of the stability of steady states and
critical phenomena for the spherically symmetric Einstein–Vlasov system”, Class. Quantum
Grav., 23, 3659–3677, (2006). [![]() ![]() |
![]() |
9 | Ayal, S., and Piran, T., “Spherical collapse of a massless scalar field with semiclassical
corrections”, Phys. Rev. D, 56, 4768–4774, (1997). [![]() ![]() |
![]() |
10 | Bartnik, R., and McKinnon, J., “Particlelike Solutions of the Einstein–Yang–Mills Equations”,
Phys. Rev. Lett., 61, 141–144, (1988). [![]() |
![]() |
11 | Birmingham, D., “Choptuik scaling and quasinormal modes in the anti-de Sitter
space/conformal-field theory correspondence”, Phys. Rev. D, 64, 064024, 1–5, (2001). [![]() ![]() |
![]() |
12 | Birmingham, D., and Sen, S., “Gott Time Machines, BTZ Black Hole Formation, and Choptuik
Scaling”, Phys. Rev. Lett., 84, 1074–1077, (2000). [![]() ![]() |
![]() |
13 | Birukou, M., Husain, V., Kunstatter, G., Vaz, E., and Olivier, M., “Spherically symmetric scalar
field collapse in any dimension”, Phys. Rev. D, 65, 104036, 1–7, (2002). [![]() ![]() |
![]() |
14 | Bizoń, P., “Colored black holes”, Phys. Rev. Lett., 64, 2844–2847, (1990). [![]() |
![]() |
15 | Bizoń, P., “How to Make a Tiny Black Hole?”, Acta Cosm., 22, 81, (1996). [![]() |
![]() |
16 | Bizoń, P., “Equivariant Self-Similar Wave Maps from Minkowski Spacetime into 3-Sphere”,
Commun. Math. Phys., 215, 45–56, (2000). [![]() ![]() ![]() |
![]() |
17 | Bizoń, P., and Chmaj, T., “Formation and critical collapse of Skyrmions”, Phys. Rev. D, 58,
041501, 1–4, (1998). [![]() ![]() |
![]() |
18 | Bizoń, P., and Chmaj, T., “Remark on formation of colored black holes via fine-tuning”, Phys.
Rev. D, 61, 067501, 1–2, (2000). [![]() ![]() |
![]() |
19 | Bizoń, P., Chmaj, T., Rostworowski, A., Schmidt, B.G., and Tabor, Z., “On vacuum
gravitational collapse in nine dimensions”, Phys. Rev. D, 72, 121502, 1–4, (2005). [![]() ![]() |
![]() |
20 | Bizoń, P., Chmaj, T., and Schmidt, B.G., “Critical Behavior in Vacuum Gravitational Collapse
in 4+1 Dimensions”, Phys. Rev. Lett., 95, 071102, 1–4, (2005). [![]() ![]() |
![]() |
21 | Bizoń, P., Chmaj, T., and Schmidt, B.G., “Codimension-Two Critical Behavior in Vacuum
Gravitational Collapse”, Phys. Rev. Lett., 97, 131101, 1–4, (2006). [![]() ![]() |
![]() |
22 | Bizoń, P., Chmaj, T., and Tabor, Z., “Equivalence of critical collapse of non-Abelian fields”,
Phys. Rev. D, 59, 104003, 1–3, (1999). [![]() ![]() |
![]() |
23 | Bizoń, P., Chmaj, T., and Tabor, Z., “Dispersion and collapse of wave maps”, Nonlinearity,
13, 1411–1423, (2000). [![]() ![]() |
![]() |
24 | Bizoń, P., Chmaj, T., and Tabor, Z., “Formation of singularities for equivariant
(2+1)-dimensional wave maps into the 2-sphere”, Nonlinearity, 14, 1041–1053, (2001). [![]() ![]() |
![]() |
25 | Bizoń, P., Szybka, S.J., and Wasserman, A., “Periodic self-similar wave maps coupled to
gravity”, Phys. Rev. D, 69, 064014, 1–6, (2004). [![]() ![]() |
![]() |
26 | Bizoń, P., and Tabor, Z., “On blowup for Yang–Mills fields”, Phys. Rev. D, 64, 121701, 1–4,
(2001). [![]() ![]() |
![]() |
27 | Bizoń, P., and Wasserman, A., “Self-similar spherically symmetric wave maps coupled to
gravity”, Phys. Rev. D, 62, 084031, 1–7, (2000). [![]() ![]() |
![]() |
28 | Bizoń, P., and Wasserman, A., “On the existence of self-similar spherically symmetric wave
maps coupled to gravity”, Class. Quantum Grav., 19, 3309–3321, (2002). [![]() ![]() |
![]() |
29 | Bland, J., and Kunstatter, G., “The 5-D Choptuik critical exponent and holography”, Phys.
Rev. D, 75, 101501, 1–4, (2007). [![]() ![]() |
![]() |
30 | Bland, J., Preston, B., Becker, M., Kunstatter, G., and Husain, V., “Dimension dependence of
the critical exponent in spherically symmetric gravitational collapse”, Class. Quantum Grav.,
22, 5355–5364, (2005). [![]() ![]() |
![]() |
31 | Bose, S., Parker, L., and Peleg, Y., “Predictability and semiclassical approximation at the onset
of black hole formation”, Phys. Rev. D, 54, 7490–7505, (1996). [![]() ![]() |
![]() |
32 | Brady, P.R., “Analytic example of critical behaviour in scalar field collapse”, Class. Quantum
Grav., 11, 1255–1260, (1994). [![]() ![]() |
![]() |
33 | Brady, P.R., and Cai, M.J., “Critical phenomena in gravitational collapse”, in Piran, T.,
ed., The Eighth Marcel Grossmann Meeting on Recent Developments in Theoretical and
Experimental General Relativity, Gravitation and Relativistic Field Theories, Proceedings of
the meeting held at the Hebrew University of Jerusalem, June 22 – 27, 1997, pp. 689–704,
(World Scientific, Singapore, 1999). [![]() |
![]() |
34 | Brady, P.R., Chambers, C.M., and Gonçalves, S.M.C.V., “Phases of massive scalar field
collapse”, Phys. Rev. D, 56, R6057–R6061, (1997). [![]() ![]() ![]() |
![]() |
35 | Brady, P.R., Choptuik, M.W., Gundlach, C., and Neilsen, D.W., “Black-hole threshold solutions
in stiff fluid collapse”, Class. Quantum Grav., 19, 6359, (2002). [![]() ![]() |
![]() |
36 | Brady, P.R., and Ottewill, A.C., “Quantum corrections to critical phenomena in gravitational
collapse”, Phys. Rev. D, 58, 024006, 1–6, (1998). [![]() ![]() |
![]() |
37 | Burko, L.M., “Black-Hole Singularities: A New Critical Phenomenon”, Phys. Rev. Lett., 90,
121101, 1–4, (2003). [![]() ![]() |
![]() |
38 | Cahill, M.E., and Taub, A.H., “Spherically symmetric similarity solutions of the Einstein field
equations for a perfect fluid”, Commun. Math. Phys., 21, 1–40, (1971). [![]() ![]() |
![]() |
39 | Carlip, S., “The (2+1)-dimensional black hole”, Class. Quantum Grav., 12, 2853–2879, (1995).
[![]() ![]() |
![]() |
40 | Carr, B.J., and Coley, A.A., “Complete classification of spherically symmetric self-similar
perfect fluid solutions”, Phys. Rev. D, 62, 044023, 1–25, (2000). [![]() ![]() |
![]() |
41 | Carr, B.J., Coley, A.A., Goliath, M., Nilsson, U.S., and Uggla, C., “Critical phenomena and
a new class of self-similar spherically symmetric perfect-fluid solutions”, Phys. Rev. D, 61,
081502, 1–5, (2000). [![]() ![]() |
![]() |
42 | Carr, B.J., and Gundlach, C., “Spacetime structure of self-similar spherically symmetric perfect
fluid solutions”, Phys. Rev. D, 67, 024035, 1–13, (2003). [![]() ![]() |
![]() |
43 | Cavaglià, M., Clément, G., and Fabbri, A., “Approximately self-similar critical collapse in
2+1 dimensions”, Phys. Rev. D, 70, 044010, 1–5, (2004). [![]() ![]() |
![]() |
44 | Caveny, S.A., and Matzner, R.A., “Adaptive event horizon tracking and critical phenomena in
binary black hole coalescence”, Phys. Rev. D, 68, 104003, 1–13, (2003). [![]() ![]() |
![]() |
45 | Chiba, T., and Siino, M., “Disappearance of black hole criticality in semiclassical general
relativity”, Mod. Phys. Lett. A, 12, 709–718, (1997). [![]() ![]() |
![]() |
46 | Choptuik, M.W., personal communication. |
![]() |
47 | Choptuik, M.W., “ ‘Critical’ behavior in massless scalar field collapse”, in d’Inverno, R.A., ed.,
Approaches to Numerical Relativity, Proceedings of the International Workshop on Numerical
Relativity, Southampton, December 1991, p. 202, (Cambridge University Press, Cambridge;
New York, 1992). [![]() |
![]() |
48 | Choptuik, M.W., “Universality and scaling in gravitational collapse of a massless scalar field”,
Phys. Rev. Lett., 70, 9–12, (1993). [![]() ![]() |
![]() |
49 | Choptuik, M.W., “Critical behavior in scalar field collapse”, in Hobill, D., Burd, A., and Coley, A., eds., Deterministic Chaos in General Relativity, Proceedings of a NATO Advanced Research Workshop on Deterministic Chaos in General Relativity, held July 25 – 30, 1993, in Kananaskis, Alberta, Canada, p. 155, (Plenum Press, New York, 1994). |
![]() |
50 | Choptuik, M.W., “The (Unstable) Threshold of Black Hole Formation”, in Dadhich, N., and
Narlikar, J.V., eds., Gravitation and Relativity: At the Turn of the Millenium, Proceedings
of the 15th International Conference on General Relativity and Gravitation (GR-15), held at
IUCAA, Pune, India, December 16 – 21, 1997, pp. 67–85, (IUCAA, Pune, 1998). [![]() |
![]() |
51 | Choptuik, M.W., “Critical behavior in gravitational collapse”, Prog. Theor. Phys. Suppl., 136,
353–365, (1999). [![]() |
![]() |
52 | Choptuik, M.W., Chmaj, T., and Bizoń, P., “Critical Behavior in Gravitational Collapse of a
Yang–Mills Field”, Phys. Rev. Lett., 77, 424–427, (1996). [![]() ![]() |
![]() |
53 | Choptuik, M.W., Hirschmann, E.W., and Liebling, S.L., “Instability of an ‘approximate black
hole’ ”, Phys. Rev. D, 55, 6014–6018, (1997). [![]() ![]() |
![]() |
54 | Choptuik, M.W., Hirschmann, E.W., Liebling, S.L., and Pretorius, F., “Critical collapse of
the massless scalar field in axisymmetry”, Phys. Rev. D, 68, 044007, 1–9, (2003). [![]() ![]() |
![]() |
55 | Choptuik, M.W., Hirschmann, E.W., Liebling, S.L., and Pretorius, F., “Critical Collapse of a
Complex Scalar Field with Angular Momentum”, Phys. Rev. Lett., 93, 131101, 1–4, (2004).
[![]() ![]() |
![]() |
56 | Choptuik, M.W., Hirschmann, E.W., and Marsa, R.L., “New critical behavior in
Einstein-Yang-Mills collapse”, Phys. Rev. D, 60, 124011, 1–9, (1999). [![]() ![]() |
![]() |
57 | Christodoulou, D., “Violation of cosmic censorship in the gravitational collapse of a dust cloud”,
Commun. Math. Phys., 93, 171–195, (1984). [![]() ![]() |
![]() |
58 | Christodoulou, D., “The problem of a self-gravitating scalar field”, Commun. Math. Phys.,
105, 337–361, (1986). [![]() ![]() |
![]() |
59 | Christodoulou, D., “A mathematical theory of gravitational collapse”, Commun. Math. Phys.,
109, 613–647, (1987). [![]() ![]() |
![]() |
60 | Christodoulou, D., “The formation of black holes and singularities in spherically symmetric
gravitational collapse”, Commun. Pure Appl. Math., 44, 339–373, (1991). [![]() |
![]() |
61 | Christodoulou, D., “Bounded Variation Solutions of the Spherically Symmetric Einstein-Scalar
Field Equations”, Commun. Pure Appl. Math., 46, 1131–1220, (1993). [![]() |
![]() |
62 | Christodoulou, D., “Examples of Naked Singularity Formation in the Gravitational Collapse
of a Scalar Field”, Ann. Math. (2), 140, 607–653, (1994). [![]() |
![]() |
63 | Christodoulou, D., “The Instability of Naked Singularities in the Gravitational Collapse of a
Scalar Field”, Ann. Math. (2), 149, 183–217, (1999). [![]() |
![]() |
64 | Clément, G., and Fabbri, A., “Analytical treatment of critical collapse in (2+1)-dimensional
AdS spacetime: a toy model”, Class. Quantum Grav., 18, 3665–3680, (2001). [![]() ![]() |
![]() |
65 | Clément, G., and Fabbri, A., “Critical collapse in (2+1)-dimensional AdS spacetime:
quasi-CSS solutions and linear perturbations”, Nucl. Phys. B, 630, 269–292, (2002). [![]() ![]() |
![]() |
66 | Clément, G., and Hayward, S.A., “Comment on ‘An extreme critical space-time: echoing
and black-hole perturbations’ ”, Class. Quantum Grav., 18, 4715–4716, (2001). [![]() ![]() |
![]() |
67 | Donninger, R., and Aichelburg, P.C., “A note on the eigenvalues for equivariant maps of the
SU(2) sigma-model”, arXiv e-print, (2006). [![]() |
![]() |
68 | Donninger, R., and Aichelburg, P.C., “On the mode stability of a self-similar wave map”, J.
Math. Phys., 49, 043515, (2008). [![]() ![]() |
![]() |
69 | Eardley, D.M., Hirschmann, E.W., and Horne, J.H., “S duality at the black hole threshold in
gravitational collapse”, Phys. Rev. D, 52, R5397–R5401, (1995). [![]() ![]() |
![]() |
70 | Eardley, D.M., and Moncrief, V., “The Global Existence of Yang–Mills–Higgs Fields in
4-Dimensional Minkowski Space. I. Local Existence and Smoothness Properties”, Commun.
Math. Phys., 83, 171–191, (1982). [![]() |
![]() |
71 | Eggers, J., and Fontelos, M.A., “The role of self-similarity in singularities of partial differential
equations”, Nonlinearity, 22, R1–R44, (2009). [![]() ![]() |
![]() |
72 | Evans, C.R., and Coleman, J.S., “Critical Phenomena and Self-Similarity in the Gravitational
Collapse of Radiation Fluid”, Phys. Rev. Lett., 72, 1782–1785, (1994). [![]() ![]() |
![]() |
73 | Frolov, A.V., “Perturbations and critical behavior in the self-similar gravitational collapse of a
massless scalar field”, Phys. Rev. D, 56, 6433–6438, (1997). [![]() ![]() |
![]() |
74 | Frolov, A.V., “Critical collapse beyond spherical symmetry: General perturbations of the
Roberts solution”, Phys. Rev. D, 59, 104011, 1–7, (1999). [![]() ![]() |
![]() |
75 | Frolov, A.V., “Self-similar collapse of scalar field in higher dimensions”, Class. Quantum Grav.,
16, 407–417, (1999). [![]() ![]() |
![]() |
76 | Frolov, A.V., “Continuous self-similarity breaking in critical collapse”, Phys. Rev. D, 61,
084006, 1–14, (2000). [![]() ![]() |
![]() |
77 | Frolov, A.V., and Pen, U.-L., “The naked singularity in the global structure of critical collapse
spacetimes”, Phys. Rev. D, 68, 124024, 1–6, (2003). [![]() ![]() |
![]() |
78 | Frolov, V.P., “Merger transitions in brane-black-hole systems: Criticality, scaling and
self-similarity”, Phys. Rev. D, 74, 044006, 1–9, (2006). [![]() ![]() |
![]() |
79 | Frolov, V.P., Larsen, A.L., and Christensen, M., “Domain wall interacting with a black
hole: A new example of critical phenomena”, Phys. Rev. D, 59, 125008, 1–8, (1999). [![]() ![]() |
![]() |
80 | Garfinkle, D., “Choptuik scaling in null coordinates”, Phys. Rev. D, 51, 5558–5561, (1995).
[![]() ![]() ![]() |
![]() |
81 | Garfinkle, D., “Choptuik scaling and the scale invariance of Einstein’s equation”, Phys. Rev.
D, 56, 3169–3173, (1997). [![]() ![]() |
![]() |
82 | Garfinkle, D., “Exact solution for (2+1)-dimensional critical collapse”, Phys. Rev. D, 63,
044007, 1–5, (2001). [![]() ![]() |
![]() |
83 | Garfinkle, D., Cutler, C., and Duncan, G.C., “Choptuik scaling in six dimensions”, Phys. Rev.
D, 60, 104007, 1–5, (1999). [![]() ![]() ![]() |
![]() |
84 | Garfinkle, D., and Duncan, G.C., “Scaling of curvature in subcritical gravitational collapse”,
Phys. Rev. D, 58, 064024, 1–4, (1998). [![]() ![]() |
![]() |
85 | Garfinkle, D., and Gundlach, C., “Symmetry-seeking spacetime coordinates”, Class. Quantum
Grav., 16, 4111–4123, (1999). [![]() ![]() |
![]() |
86 | Garfinkle, D., and Gundlach, C., “Perturbations of an exact solution for 2+1-dimensional
critical collapse”, Phys. Rev. D, 66, 044015, 1–4, (2002). [![]() ![]() |
![]() |
87 | Garfinkle, D., Gundlach, C., and Martín-García, J.M., “Angular momentum near the
black hole threshold in scalar field collapse”, Phys. Rev. D, 59, 104012, 1–5, (1999). [![]() ![]() |
![]() |
88 | Garfinkle, D., and Isenberg, J., “Numerical studies of the behavior of Ricci flow”, in Chang,
S.-C., Chow, B., Chu, S.-C., and Lin, C.-S., eds., Geometric Evolution Equations, National
Center for Theoretical Sciences Workshop on Geometric Evolution Equations, National Tsing
Hua University, Hsinchu, Taiwan, July 15 – August 14, 2002, Contemporary Mathematics, vol.
367, p. 103, (American Mathematical Society, Providence, RI, 2004). [![]() |
![]() |
89 | Garfinkle, D., and Isenberg, J., “The modelling of degenerate neck pinch singularities in Ricci
flow by Bryant solitons”, J. Math. Phys., 49, 073505, (2007). [![]() ![]() |
![]() |
90 | Garfinkle, D., Mann, R., and Vuille, C., “Critical collapse of a massive vector field”, Phys. Rev.
D, 68, 064015, 1–6, (2003). [![]() ![]() |
![]() |
91 | Garfinkle, D., and Meyer, K., “Scale invariance and critical gravitational collapse”, Phys. Rev.
D, 59, 064003, 1–5, (1999). [![]() ![]() |
![]() |
92 | Giddings, S.B., “Quantum mechanics of black holes”, arXiv e-print, (1994). [![]() |
![]() |
93 | Goode, S.W., Coley, A.A., and Wainwright, J., “The isotropic singularity in cosmology”, Class.
Quantum Grav., 9, 445–455, (1992). [![]() |
![]() |
94 | Green, A.M., and Liddle, A.R., “Critical collapse and the primordial black hole initial mass
function”, Phys. Rev. D, 60, 063509, 1–8, (1999). [![]() ![]() |
![]() |
95 | Gundlach, C., “The Choptuik Spacetime as an Eigenvalue Problem”, Phys. Rev. Lett., 75,
3214–3217, (1995). [![]() ![]() |
![]() |
96 | Gundlach, C., “Critical phenomena in gravitational collapse”, in Chruściel, P.T., ed.,
Mathematics of Gravitation, Part I: Lorentzian Geometry and Einstein Equations, Proceedings
of the Workshop on Mathematical Aspects of Theories of Gravitation, held in Warsaw, Poland,
February 29 – March 30, 1996, Banach Center Publications, vol. 41, pp. 143–152, (Polish
Academy of Sciences, Institute of Mathematics, Warsaw, 1997). [![]() |
![]() |
97 | Gundlach, C., “Echoing and scaling in Einstein-Yang-Mills critical collapse”, Phys. Rev. D, 55,
6002–6013, (1997). [![]() ![]() |
![]() |
98 | Gundlach, C., “Understanding critical collapse of a scalar field”, Phys. Rev. D, 55, 695–713,
(1997). [![]() ![]() |
![]() |
99 | Gundlach, C., “Angular momentum at the black hole threshold”, Phys. Rev. D, 57, 7080–7083,
(1998). [![]() ![]() |
![]() |
100 | Gundlach, C., “Critical phenomena in gravitational collapse”, Adv. Theor. Math. Phys., 2,
1–49, (1998). [![]() |
![]() |
101 | Gundlach, C., “Nonspherical perturbations of critical collapse and cosmic censorship”, Phys.
Rev. D, 57, 7075–7079, (1998). [![]() ![]() |
![]() |
102 | Gundlach, C., “Critical Phenomena in Gravitational Collapse”, Living Rev. Relativity, 2,
lrr-1999-4, (1999). URL (cited on 1 February 2003): http://www.livingreviews.org/lrr-1999-4. |
![]() |
103 | Gundlach, C., “Critical gravitational collapse of a perfect fluid: Nonspherical perturbations”,
Phys. Rev. D, 65, 084021, 1–22, (2002). [![]() ![]() |
![]() |
104 | Gundlach, C., “Critical gravitational collapse with angular momentum: from critical exponents
to universal scaling functions”, Phys. Rev. D, 65, 064019, (2002). [![]() ![]() |
![]() |
105 | Gundlach, C., “Critical phenomena in gravitational collapse”, Phys. Rep., 376, 339–405, (2003).
[![]() ![]() |
![]() |
106 | Gundlach, C., and Martín-García, J.M., “Charge scaling and universality in critical
collapse”, Phys. Rev. D, 54, 7353–7360, (1996). [![]() ![]() |
![]() |
107 | Gundlach, C., and Martín-García, J.M., “Kinematics of discretely self-similar spherically
symmetric spacetimes”, Phys. Rev. D, 68, 064019, 1–11, (2003). [![]() ![]() |
![]() |
108 | Gundlach, C., and Martín-García, J.M., “Well-posedness of formulations of the Einstein
equations with dynamical lapse and shift conditions”, Phys. Rev. D, 74, 024016, 1–19, (2006).
[![]() ![]() |
![]() |
109 | Gundlach, C., Price, R.H., and Pullin, J., “Late-time behavior of stellar collapse and explosions.
II. Nonlinear evolution”, Phys. Rev. D, 49, 890–899, (1994). [![]() ![]() ![]() |
![]() |
110 | Hamadé, R.S., Horne, J.H., and Stewart, J.M., “Continuous self-similarity and S-duality”,
Class. Quantum Grav., 13, 2241–2253, (1996). [![]() ![]() ![]() |
![]() |
111 | Hamadé, R.S., and Stewart, J.M., “The spherically symmetric collapse of a massless scalar
field”, Class. Quantum Grav., 13, 497–512, (1996). [![]() ![]() ![]() |
![]() |
112 | Hara, T., Koike, T., and Adachi, S., “Renormalization group and critical behavior in
gravitational collapse”, arXiv e-print, (1996). [![]() |
![]() |
113 | Harada, T., “Final fate of the spherically symmetric collapse of a perfect fluid”, Phys. Rev. D,
58, 104015, 1–10, (1998). [![]() ![]() |
![]() |
114 | Harada, T., “Stability criterion for self-similar solutions with perfect fluids in general relativity”,
Class. Quantum Grav., 18, 4549–4567, (2001). [![]() ![]() |
![]() |
115 | Harada, T., and Maeda, H., “Convergence to a self-similar solution in general relativistic
gravitational collapse”, Phys. Rev. D, 63, 084022, 1–14, (2001). [![]() ![]() |
![]() |
116 | Harada, T., and Maeda, H., “Critical phenomena in Newtonian gravity”, Phys. Rev. D, 64,
124024, 1–7, (2001). [![]() ![]() |
![]() |
117 | Harada, T., Maeda, H., and Semelin, B., “Criticality and convergence in Newtonian collapse”,
Phys. Rev. D, 67, 084003, 1–10, (2003). [![]() ![]() |
![]() |
118 | Harada, T., and Mahajan, A., “Analytical solutions for black-hole critical behaviour”, Gen.
Relativ. Gravit., 39, 1847–1854, (2007). [![]() ![]() |
![]() |
119 | Hawke, I., and Stewart, J.M., “The dynamics of primordial black-hole formation”, Class.
Quantum Grav., 19, 3687–3707, (2002). [![]() |
![]() |
120 | Hawley, S.H., and Choptuik, M.W., “Boson stars driven to the brink of black hole formation”,
Phys. Rev. D, 62, 104024, 1–19, (2000). [![]() ![]() |
![]() |
121 | Hayward, S.A., “An extreme critical spacetime: echoing and black-hole perturbations”, Class.
Quantum Grav., 17, 4021–4030, (2000). [![]() ![]() |
![]() |
122 | Hirschmann, E.W., and Eardley, D.M., “Critical exponents and stability at the black
hole threshold for a complex scalar field”, Phys. Rev. D, 52, 5850–5856, (1995). [![]() ![]() |
![]() |
123 | Hirschmann, E.W., and Eardley, D.M., “Universal scaling and echoing in gravitational collapse
of a complex scalar field”, Phys. Rev. D, 51, 4198–4207, (1995). [![]() ![]() |
![]() |
124 | Hirschmann, E.W., and Eardley, D.M., “Criticality and bifurcation in the gravitational collapse
of a self-coupled scalar field”, Phys. Rev. D, 56, 4696–4705, (1997). [![]() ![]() |
![]() |
125 | Hirschmann, E.W., Wang, A., and Wu, Y., “Collapse of a Scalar Field in 2+1 Gravity”, Class.
Quantum Grav., 21, 1791–1824, (2004). [![]() ![]() |
![]() |
126 | Hod, S., and Piran, T., “Critical behavior and universality in gravitational collapse of a charged
scalar field”, Phys. Rev. D, 55, 3485–3496, (1997). [![]() ![]() ![]() |
![]() |
127 | Hod, S., and Piran, T., “Fine-structure of Choptuik’s mass-scaling relation”, Phys. Rev. D, 55,
440–442, (1997). [![]() ![]() |
![]() |
128 | Honda, E.P., and Choptuik, M.W., “Fine structure of oscillons in the spherically symmetric ϕ4
Klein-Gordon model”, Phys. Rev. D, 65, 084037, 1–12, (2002). [![]() ![]() |
![]() |
129 | Horne, J.H., “Critical behavior in black hole collapse”, Matters of Gravity(7), 14–15, (1996).
[![]() |
![]() |
130 | Horowitz, G.T., and Hubeny, V.E., “Quasinormal modes of AdS black holes and the approach
to thermal equilibrium”, Phys. Rev. D, 62, 024027, 1–11, (2000). [![]() ![]() |
![]() |
131 | Husa, S., Lechner, C., Pürrer, M., Thornburg, J., and Aichelburg, P.C., “Type II critical
collapse of a self-gravitating nonlinear σ model”, Phys. Rev. D, 62, 104007, 1–11, (2000). [![]() ![]() ![]() |
![]() |
132 | Husain, V., “Critical Behaviour in Quantum Gravitational Collapse”, Adv. Sci. Lett., 2,
214–220, (2009). [![]() ![]() |
![]() |
133 | Husain, V., Kunstatter, G., Preston, B., and Birukou, M., “Anti-de Sitter gravitational
collapse”, Class. Quantum Grav., 20, L23–L29, (2003). [![]() ![]() |
![]() |
134 | Husain, V., and Olivier, M., “Scalar field collapse in three-dimensional AdS spacetime”, Class.
Quantum Grav., 18, L1–L9, (2001). [![]() ![]() |
![]() |
135 | Husain, V., and Seahra, S.S., “Ricci flows, wormholes and critical phenomena”, Class. Quantum
Grav., 25, 222002, (2008). [![]() ![]() |
![]() |
136 | Jin, K.-J., and Suen, W.-M., “Critical Phenomena in Head-On Collisions of Neutron Stars”,
Phys. Rev. Lett., 98, 131101, 1–4, (2007). [![]() ![]() |
![]() |
137 | Kiem, Y., “Phase Transition in Spherically Symmetric Gravitational Collapse of a Massless
Scalar Field”, arXiv e-print, (1994). [![]() |
![]() |
138 | Koike, T., Hara, T., and Adachi, S., “Critical Behavior in Gravitational Collapse of Radiation
Fluid: A Renormalization Group (Linear Perturbation) Analysis”, Phys. Rev. Lett., 74,
5170–5173, (1995). [![]() ![]() |
![]() |
139 | Koike, T., Hara, T., and Adachi, S., “Critical behavior in gravitational collapse of a perfect fluid”, Phys. Rev. D, 59, 104008, 1–9, (1999). |
![]() |
140 | Kol, B., “Choptuik Scaling and The Merger Transition”, J. High Energy Phys., 2006(10), 017,
1–18, (2006). [![]() ![]() |
![]() |
141 | Lai, C.W., A Numerical Study of Boson Stars, Ph.D. Thesis, (University of British Columbia,
Vancouver, 2004). [![]() ![]() |
![]() |
142 | Lai, C.W., and Choptuik, M.W., “Final Fate of Subcritical Evolutions of Boson Stars”, arXiv
e-print, (2007). [![]() |
![]() |
143 | Lavrelashvili, G., and Maison, D., “A remark on the instability of the Bartnik–McKinnon
solutions”, Phys. Lett. B, 343, 214–217, (1995). [![]() |
![]() |
144 | Lechner, C., Staticity, self-similarity and critical phenomena in a self-gravitating nonlinear
sigma model, Ph.D. Thesis, (University of Vienna, Vienna, 2001). [![]() |
![]() |
145 | Lechner, C., Thornburg, J., Husa, S., and Aichelburg, P.C., “A new transition between discrete
and continuous self-similarity in critical gravitational collapse”, Phys. Rev. D, 65, 081501, 1–4,
(2002). [![]() ![]() |
![]() |
146 | Levin, J., “Gravity Waves, Chaos, and Spinning Compact Binaries”, Phys. Rev. Lett., 84,
3515–3518, (2000). [![]() ![]() |
![]() |
147 | Liebling, S.L., “Multiply unstable black hole critical solutions”, Phys. Rev. D, 58, 084015, 1–8,
(1998). [![]() ![]() |
![]() |
148 | Liebling, S.L., “Critical phenomena inside global monopoles”, Phys. Rev. D, 60, 061502, 1–5,
(1999). [![]() ![]() |
![]() |
149 | Liebling, S.L., “Singularity threshold of the nonlinear sigma model using 3D adaptive mesh
refinement”, Phys. Rev. D, 66, 041703, 1–5, (2002). [![]() ![]() |
![]() |
150 | Liebling, S.L., and Choptuik, M.W., “Black Hole Criticality in the Brans–Dicke Model”, Phys.
Rev. Lett., 77, 1424–1427, (1996). [![]() ![]() |
![]() |
151 | Liebling, S.L., Hirschmann, E.W., and Isenberg, J.A., “Critical phenomena in nonlinear sigma
models”, J. Math. Phys., 41(8), 5691–5700, (2000). [![]() ![]() |
![]() |
152 | Mahajan, A., Harada, T., Joshi, P., and Nakao, K., “Critical Collapse of Einstein Cluster”,
Prog. Theor. Phys., 118, 865–878, (2007). [![]() ![]() |
![]() |
153 | Maison, D., “Non-universality of critical behaviour in spherically symmetric gravitational
collapse”, Phys. Lett. B, 366, 82–84, (1996). [![]() ![]() |
![]() |
154 | Martín-García, J.M., and Gundlach, C., “All nonspherical perturbations of the Choptuik
spacetime decay”, Phys. Rev. D, 59, 064031, 1–19, (1999). [![]() ![]() |
![]() |
155 | Martín-García, J.M., and Gundlach, C., “Self-similar spherically symmetric solutions
of the massless Einstein–Vlasov system”, Phys. Rev. D, 65, 084026, 1–18, (2002). [![]() ![]() |
![]() |
156 | Martín-García, J.M., and Gundlach, C., “Critical Phenomena in Gravitational Collapse: The Role of Angular Momentum”, in Fernández-Jambrina, L., and González-Romero, L.M., eds., Current Trends in Relativistic Astrophysics: Theoretical, Numerical, Observational, Proceedings of the 24th Spanish Relativity Meeting on Relativistic Astrophysics, Madrid, 2001, Lecture Notes in Physics, vol. 617, pp. 68–86, (Springer, Berlin; New York, 2003). |
![]() |
157 | Martín-García, J.M., and Gundlach, C., “Global structure of Choptuik’s critical solution
in scalar field collapse”, Phys. Rev. D, 68, 024011, 1–25, (2003). [![]() ![]() |
![]() |
158 | Millward, R.S., and Hirschmann, E.W., “Critical behavior of gravitating sphalerons”, Phys.
Rev. D, 68, 024017, 1–12, (2003). [![]() ![]() |
![]() |
159 | Musco, I., Miller, J.C., and Polnarev, A.G., “Primordial black hole formation in the radiative
era: investigation of the critical nature of the collapse”, Class. Quantum Grav., 26, 235001,
(2009). [![]() ![]() |
![]() |
160 | Musco, I., Miller, J.C., and Rezzolla, L., “Computations of primordial black-hole formation”,
Class. Quantum Grav., 22, 1405–1424, (2005). [![]() ![]() |
![]() |
161 | Neilsen, D.W., and Choptuik, M.W., “Critical phenomena in perfect fluids”, Class. Quantum
Grav., 17, 761–782, (2000). [![]() ![]() |
![]() |
162 | Neilsen, D.W., and Choptuik, M.W., “Ultrarelativistic fluid dynamics”, Class. Quantum Grav.,
17, 733–759, (2000). [![]() ![]() |
![]() |
163 | Niemeyer, J.C., and Jedamzik, K., “Near-Critical Gravitational Collapse and the Initial
Mass Function of Primordial Black Holes”, Phys. Rev. Lett., 80, 5481–5484, (1998). [![]() ![]() |
![]() |
164 | Niemeyer, J.C., and Jedamzik, K., “Dynamics of primordial black hole formation”, Phys. Rev.
D, 59, 124013, 1–8, (1999). [![]() ![]() |
![]() |
165 | Noble, S.C., A Numerical Study of Relativistic Fluid Collapse, Ph.D. Thesis, (University of
Texas at Austin, Austin, 2003). [![]() |
![]() |
166 | Noble, S.C., and Choptuik, M.W., “Type II critical phenomena of neutron star collapse”, Phys.
Rev. D, 78, 064059, (2008). [![]() ![]() |
![]() |
167 | Novak, J., “Velocity-induced collapses of stable neutron stars”, Astron. Astrophys., 376,
606–613, (2001). [![]() ![]() |
![]() |
168 | Olabarrieta, I., and Choptuik, M.W., “Critical phenomena at the threshold of black hole
formation for collisionless matter in spherical symmetry”, Phys. Rev. D, 65, 024007, 1–10,
(2001). [![]() ![]() |
![]() |
169 | Olabarrieta, I., Ventrella, J.F., Choptuik, M.W., and Unruh, W.G., “Critical behavior in the
gravitational collapse of a scalar field with angular momentum in spherical symmetry”, Phys.
Rev. D, 76, 124014, (2007). [![]() ![]() |
![]() |
170 | Oliveira-Neto, G., and Takakura, F.I., “Wyman’s solution, self-similarity, and critical
behaviour”, J. Math. Phys., 46, 062503, 1–6, (2005). [![]() ![]() |
![]() |
171 | Ori, A., and Piran, T., “Naked singularities in self-similar spherical gravitational collapse”,
Phys. Rev. Lett., 59, 2137–2140, (1987). [![]() |
![]() |
172 | Ori, A., and Piran, T., “Naked singularities and other features of self-similar general-relativistic
gravitational collapse”, Phys. Rev. D, 42, 1068–1090, (1990). [![]() |
![]() |
173 | Oshiro, Y., Nakamura, K., and Tomimatsu, A., “Critical behavior of black hole formation in a
scalar wave Collapse”, Prog. Theor. Phys., 91, 1265–1270, (1994). [![]() ![]() |
![]() |
174 | Peleg, Y., Bose, S., and Parker, L., “Choptuik scaling and quantum effects in 2D dilaton
gravity”, Phys. Rev. D, 55, 4525–4528, (1997). [![]() ![]() |
![]() |
175 | Peleg, Y., and Steif, A.R., “Phase transition for gravitationally collapsing dust shells in 2+1
dimensions”, Phys. Rev. D, 51, R3992–R3996, (1995). [![]() ![]() |
![]() |
176 | Petryk, R., Maxwell–Klein–Gordon Fields in Black Hole Spacetimes, Ph.D. Thesis, (University
of British Columbia, Vancouver, 2005). Related online version (cited on 15 June 2007): ![]() |
![]() |
177 | Polnarev, A.G., and Musco, I., “Curvature profiles as initial conditions for primordial black
hole formation”, Class. Quantum Grav., 24, 1405–1432, (2007). [![]() ![]() |
![]() |
178 | Pretorius, F., and Choptuik, M.W., “Gravitational collapse in 2+1 dimensional AdS
spacetime”, Phys. Rev. D, 62, 124012, 1–15, (2000). [![]() ![]() |
![]() |
179 | Pretorius, F., and Khurana, D., “Black hole mergers and unstable circular orbits”, Class.
Quantum Grav., 24, S83–S108, (2007). [![]() ![]() |
![]() |
180 | Price, R.H., and Pullin, J., “Analytic approximations to the spacetime of a critical gravitational
collapse”, Phys. Rev. D, 54, 3792–3799, (1996). [![]() ![]() |
![]() |
181 | Pullin, J., “Is there a connection between no-hair behavior and universality in gravitational
collapse?”, Phys. Lett. A, 204, 7–10, (1995). [![]() ![]() |
![]() |
182 | Pürrer, M., Husa, S., and Aichelburg, P.C., “News from critical collapse: Bondi mass, tails
and quasinormal modes”, Phys. Rev. D, 71, 104005, 1–13, (2005). [![]() ![]() |
![]() |
183 | Rein, G., Rendall, A.D., and Schaeffer, J., “Critical collapse of collisionless matter: A numerical
investigation”, Phys. Rev. D, 58, 044007, 1–8, (1998). [![]() ![]() |
![]() |
184 | Roberts, M.D., “Scalar field counterexamples to the cosmic censorship hypothesis”, Gen.
Relativ. Gravit., 21, 907–939, (1989). [![]() |
![]() |
185 | Sarbach, O., and Lehner, L., “Critical bubbles and implications for critical black strings”, Phys.
Rev. D, 71, 026002, 1–11, (2005). [![]() ![]() |
![]() |
186 | Seidel, E., and Suen, W.-M., “Oscillating soliton stars”, Phys. Rev. Lett., 66, 1659–1662, (1991).
[![]() |
![]() |
187 | Shibata, M., Okawa, H., and Yamamoto, T., “High-velocity collision of two black holes”, Phys.
Rev. D, 78, 101501(R), (2008). [![]() ![]() |
![]() |
188 | Smarr, L.L., and York Jr, J.W., “Kinematical conditions in the construction of spacetime”,
Phys. Rev. D, 17, 2529–2551, (1978). [![]() |
![]() |
189 | Snajdr, M., “Critical collapse of an ultrarelativistic fluid in the Γ → 1 limit”, Class. Quantum
Grav., 23, 3333–3352, (2006). [![]() ![]() |
![]() |
190 | Sorkin, E., and Oren, Y., “Choptuik’s scaling in higher dimensions”, Phys. Rev. D, 71, 124005,
(2005). [![]() ![]() |
![]() |
191 | Sperhake, U., Cardoso, V., Pretorius, F., Berti, E., Hinderer, T., and Yunes, N., “Cross Section,
Final Spin, and Zoom-Whirl Behavior in High-Energy Black-Hole Collisions”, Phys. Rev. Lett.,
103, 131102, (2009). [![]() ![]() |
![]() |
192 | Stevenson, R., The Spherically Symmetric Collapse of Collisionless Matter: Exploring Critical
Phenomena through Finite Volume Methods, Masters Thesis, (University of British Columbia,
Vancouver, 2005). Related online version (cited on 15 June 2007): ![]() |
![]() |
193 | Straumann, N., and Zhou, Z.-H., “Instability of a colored black hole solution”, Phys. Lett. B,
243, 33–35, (1990). [![]() |
![]() |
194 | Strominger, A., and Thorlacius, L., “Universality and scaling at the onset of quantum black
hole formation”, Phys. Rev. Lett., 72, 1584–1587, (1994). [![]() ![]() |
![]() |
195 | Szybka, S.J., “Chaotic self-similar wave maps coupled to gravity”, Phys. Rev. D, 69, 084014,
1–7, (2004). [![]() ![]() |
![]() |
196 | Szybka, S.J., and Chmaj, T., “Fractal Threshold Behavior in Vacuum Gravitational Collapse”,
Phys. Rev. Lett., 100, 101102, (2008). [![]() ![]() |
![]() |
197 | Thornburg, J., Lechner, C., Pürrer, M., Aichelburg, P.C., and Husa, S., “Type II Critical
Collapse of a Self-Gravitating Nonlinear σ Model”, in Gurzadyan, V.G., Jantzen, R.T., and
Ruffini, R., eds., The Ninth Marcel Grossmann Meeting on recent developments in theoretical
and experimental general relativity, gravitation and relativistic field theories, Proceedings of
the MGIX MM meeting held at the University of Rome ‘La Sapienza’, July 2 – 8, 2000, pp.
1645–1646, (World Scientific, Singapore; River Edge, NJ, 2001). [![]() |
![]() |
198 | Tod, P., personal communication. |
![]() |
199 | van Putten, M.H.P.M., “Approximate black holes for numerical relativity”, Phys. Rev. D, 54,
R5931–R5934, (1996). [![]() ![]() |
![]() |
200 | Ventrella, J.F., and Choptuik, M.W., “Critical phenomena in the Einstein–massless–Dirac
system”, Phys. Rev. D, 68, 044020, 1–10, (2003). [![]() ![]() |
![]() |
201 | Volkov, M.S., Brodbeck, O., Lavrelashvili, G., and Straumann, N., “The number of sphaleron
instabilities of the Bartnik–McKinnon solitons and non-Abelian black holes”, Phys. Lett. B,
349, 438–442, (1995). [![]() ![]() |
![]() |
202 | Volkov, M.S., and Gal’tsov, D.V., “Non-Abelian Einstein–Yang–Mills Black Holes”, J. Exp. Theor. Phys. Lett., 50, 346–350, (1989). |
![]() |
203 | Wald, R.M., “Gravitational Collapse and Cosmic Censorship”, arXiv e-print, (1997).
[![]() |
![]() |
204 | Wan, M.-B., Jin, K.-J., and Suen, W.-M., “Dynamical analysis of the structure of neutron
star critical collapses”, Poster version presented at the ‘2nd Course of the International School
on Astrophysical Relativity’, Erice, Italy, June 27 – July 5, 2008, conference paper, (2008).
[![]() |
![]() |
205 | Wang, A., “Critical collapse of cylindrically symmetric scalar field in four-dimensional
Einstein’s theory of gravity”, Phys. Rev. D, 68, 064006, 1–12, (2003). [![]() ![]() |
![]() |
206 | Wang, A., and de Oliveira, H.P., “Critical phenomena of collapsing massless scalar wave
packets”, Phys. Rev. D, 56, 753–761, (1997). [![]() |
![]() |
207 | Wyman, M., “Static spherically symmetric scalar fields in general relativity”, Phys. Rev. D,
24, 839–841, (1981). [![]() |
![]() |
208 | Yeomans, J.M., Statistical Mechanics of Phase Transitions, Oxford Science Publications,
(Clarendon Press; Oxford University Press, Oxford; New York, 1992). [![]() |
![]() |
209 | Yokoyama, J., “Cosmological constraints on primordial black holes produced in the near-critical
gravitational collapse”, Phys. Rev. D, 58, 107502, (1998). [![]() |
![]() |
210 | Zhou, J.-G., Müller-Kirsten, H.J.W., and Yang, M.-Z., “New look at the critical behaviour near the threshold of black hole formation in the Russo–Susskind–Thorlacius model”, Phys. Rev. D, 51, R314–R318, (1995). |
![]() |
211 | Ziprick, J., and Kunstatter, G., “Dynamical singularity resolution in spherically symmetric
black hole formation”, Phys. Rev. D, 80, 024032, (2009). [![]() ![]() |
![]() |
212 | Ziprick, J., and Kunstatter, G., “Spherically symmetric black hole
formation in Painlevé-Gullstrand coordinates”, Phys. Rev. D, 79, 101503(R), (2009). [![]() ![]() |
http://www.livingreviews.org/lrr-2007-5 | ![]() This work is licensed under a Creative Commons License. Problems/comments to |