Fetching the paper…
Reading the bibliography…
As first discovered by Choptuik, the black hole threshold in the space of initial data for general relativity shows both surprising structure and surprising simplicity.
Cahill, M.E., and Taub, A.H., “Spherically symmetric similarity solutions of the Einstein equations for a perfect fluid”, Commun. Math. Phys
1971
Earlier work this paper cites.
Smarr, L., and York Jr., J.W., “Kinematical conditions in the construction of spacetime”, Phys. Rev. D
1978
Earlier work this paper cites.
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”, Comm. Math. Phys
1982
Earlier work this paper cites.
Christodoulou, D., “Violation of cosmic censorship in the gravitational collapse of a dust cloud”, Commun. Math. Phys
1984
Earlier work this paper cites.
Christodoulou, D., “The problem of a self-gravitating scalar field”, Commun. Math. Phys
1986
Earlier work this paper cites.
Christodoulou, D., “A mathematical theory of gravitational collapse”, Commun. Math. Phys
1987
Earlier work this paper cites.
Ori, A., and Piran, T., “Naked singularities in self-similar spherical gravitational collapse”, Phys. Rev. Lett
1987
Earlier work this paper cites.
Bartnik, R., and McKinnon, J., “Particle-like solutions of the Einstein-Yang-Mills equations”, Phys. Rev. Lett
1988
Earlier work this paper cites.
Roberts, M.D., “Scalar field counterexamples to the cosmic censorship hypothesis”, Gen. Relativ. Gravit
1989
Earlier work this paper cites.
Bizoń, P., “Colored black holes”, Phys. Rev. Lett
1990
Earlier work this paper cites.
Ori, A., and Piran, T., “Naked singularities and other features of self-similar general-relativistic gravitational collapse”, Phys. Rev. D
1990
Earlier work this paper cites.
Straumann, N., and Zhou, Z.H., “Instability of a colored black hole solution”, Phys. Lett. B
1990
Earlier work this paper cites.
Volkov, M.S., and Gal’tsov, D.V., “Non-abelian Einstein-Yang-Mills black holes”, J. Exp. Theor. Phys. Lett
1990
Earlier work this paper cites.
Christodoulou, D., “The formation of black holes and singularities in spherically symmetric gravitational collapse”, Commun. Pure Appl. Math
1991
Earlier work this paper cites.
Seidel, E., and Suen, W.-M., “Oscillating soliton stars”, Phys. Rev. Lett
1991
Earlier work this paper cites.
Choptuik, M.W., “ ‘Critical’ behavior in massless scalar field collapse”, in d’Inverno, R., ed., Approaches to Numerical Relativity
1992
Earlier work this paper cites.
Goode, S.W., Coley, A.A., and Wainwright, J., “The isotropic singularity in cosmology”, Class. Quant. Grav
1992
Earlier work this paper cites.
Yeomans, J.M., Statistical Mechanics of Phase Transitions
1992
Earlier work this paper cites.
Abrahams, A.M., and Evans, C.R., “Critical behavior and scaling in vacuum axisymmetric gravitational collapse”, Phys. Rev. Lett
1993
Earlier work this paper cites.
Choptuik, M.W., “Universality and scaling in gravitational collapse of a massless scalar field”, Phys. Rev. Lett
1993
Earlier work this paper cites.
Christodoulou, D., “Bounded variation solutions of the spherically symmetric Einstein-scalar field equations”, Commun. Pure Appl. Math
1993
Earlier work this paper cites.
Abrahams, A.M., and Evans, C.R., “Universality in axisymmetric vacuum collapse”, Phys. Rev. D
1994
Earlier work this paper cites.
Choptuik, M.W., “Critical behavior in scalar field collapse”, in Hobill, D., Burd, A., and Coley, A., eds., Deterministic Chaos in General Relativity
1994
Earlier work this paper cites.
Christodoulou, D., “Examples of naked singularity formation in the gravitational collapse of a scalar field”, Ann. Math
1994
Earlier work this paper cites.
Evans, C.R., and Coleman, C.S., “Critical Phenomena and Self-Similarity in the Gravitational Collapse of Radiation Fluid”, Phys. Rev. Lett
1994
Earlier work this paper cites.
Giddings, S.B., “Quantum mechanics of black holes”, (December, 1994). Related online version (cited on 10 December 1999): http://arXiv.org/abs/hep-th/9412138 . Lectures presented at the 1994 Trieste Summer School in High Energy Physics and Cosmology
1994
Earlier work this paper cites.
Lavrelashvili, G., and Maison, D., “A remark on the instability of the Bartnik-McKinnon solutions”, Phys. Lett. B
1995
Earlier work this paper cites.
1995
Earlier work this paper cites.
Chiba, T., and Siino, M., “Disappearance of black hole criticality in semiclassical general relativity”, Mod. Phys. Lett. A
1997
Earlier work this paper cites.
Ayal, S., and Piran, T., “Spherical collapse of a mass-less scalar field with semi-classical corrections”, Phys. Rev. D
1999
Earlier work this paper cites.
Bizoń, P., “How to Make a Tiny Black Hole?”, Acta Cosmologica
1999
Earlier work this paper cites.
Bizoń, P., and Chmaj, T., “Formation and critical collapse of Skyrmions”, Phys. Rev. D
1999
Earlier work this paper cites.
Bizoń, P., and Chmaj, T., “Remark on formation of colored black holes via fine-tuning”, Phys. Rev. D
1999
Earlier work this paper cites.
Bizoń, P., Chmaj, T., and Tabor, Z., “On Equivalence of Critical Collapse of Non-Abelian Field”, Phys. Rev. D
1999
Earlier work this paper cites.
Bose, S., Parker, L., and Peleg, Y., “Predictability and semiclassical approximation at the onset of black hole formation”, Phys. Rev. D
1999
Earlier work this paper cites.
Brady, P.R., “Does scalar field collapse produce ‘zero mass’ black holes?”, Class. Quant. Grav
1999
Earlier work this paper cites.
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
1999
Earlier work this paper cites.
Brady, P.R., Chambers, C.M., and Gonçalves, S.M.C.V., “Phases of massive scalar field collapse”, Phys. Rev. D
1999
Earlier work this paper cites.
Brady, P.R., and Ottewill, A.C., “Quantum corrections to critical phenomena in gravitational collapse”, Phys. Rev. D
1999
Earlier work this paper cites.
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
1999
Earlier work this paper cites.
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
1999
Earlier work this paper cites.
Choptuik, M.W., “Critical behavior in gravitational collapse”, Prog. Theor. Phys. Suppl
1999
Earlier work this paper cites.
Choptuik, M.W., Chmaj, T., and Bizoń, P., “Critical Behavior in Gravitational Collapse of a Yang-Mills Field”, Phys. Rev. Lett
1999
Earlier work this paper cites.
Choptuik, M.W., Hirschmann, E.W., and Liebling, S.L., “Instability of an ‘Approximate black hole”’, Phys. Rev. D
1999
Earlier work this paper cites.
Choptuik, M.W., Hirschmann, E.W., and Marsa, R.L., “New critical behavior in Einstein-Yang-Mills collapse”, Phys. Rev. D
1999
Earlier work this paper cites.
Christodoulou, D., “The instability of naked singularities in the gravitational collapse of a scalar field”, Ann. Math. (2)
1999
Earlier work this paper cites.
Eardley, D.M., Hirschmann, E.W., and Horne, J.H., “ S S duality at the black hole threshold in gravitational collapse”, Phys. Rev. D
1999
Earlier work this paper cites.
Frolov, A.V., “Perturbations and critical behavior in the self-similar gravitational collapse of a massless scalar field”, Phys. Rev. D
1999
Earlier work this paper cites.
Frolov, A.V., “Critical Collapse Beyond Spherical Symmetry: General Perturbations of the Roberts Solution”, Phys. Rev. D
1999
Earlier work this paper cites.
Frolov, A.V., “Continuous self-similarity breaking in critical collapse”, Phys. Rev. D
1999
Earlier work this paper cites.
Garfinkle, D., “Choptuik scaling in null coordinates”, Phys. Rev. D
1999
Earlier work this paper cites.
Garfinkle, D., “Choptuik scaling and the scale invariance of Einstein’s equation”, Phys. Rev. D
1999
Earlier work this paper cites.
Garfinkle, D., Cutler, C., and Duncan, G.C., “Choptuik scaling in six dimensions”, Phys. Rev. D
1999
Earlier work this paper cites.
Garfinkle, D., and Duncan, G.C., “Scaling of curvature in sub-critical gravitational collapse”, Phys. Rev. D
1999
Earlier work this paper cites.
Garfinkle, D., and Gundlach, C., “Symmetry-seeking spacetime coordinates”, Class. Quant. Grav
1999
Earlier work this paper cites.
Garfinkle, D., Gundlach, C., and Martín-García, J.M., “Angular momentum near the black hole threshold in scalar field collapse”, Phys. Rev. D
1999
Earlier work this paper cites.
Garfinkle, D., and Meyer, K., “Scale invariance and critical gravitational collapse”, Phys. Rev. D
1999
Earlier work this paper cites.
Gundlach, C., “The Choptuik Spacetime as an Eigenvalue Problem”, Phys. Rev. Lett
1999
Earlier work this paper cites.
Gundlach, C., “Critical phenomena in gravitational collapse”, in Chruściel, P.T., ed., Mathematics of Gravitation, Part I: Lorentzian Geometry and Einstein Equations
1999
Earlier work this paper cites.
Gundlach, C., “Echoing and scaling in Einstein-Yang-Mills critical collapse”, Phys. Rev. D
1999
Earlier work this paper cites.
Gundlach, C., “Understanding critical collapse of a scalar field”, Phys. Rev. D
1999
Earlier work this paper cites.
Gundlach, C., “Angular momentum at the black hole threshold”, Phys. Rev. D
1999
Earlier work this paper cites.
Gundlach, C., “Critical phenomena in gravitational collapse”, Adv. Theor. Math. Phys
1999
Earlier work this paper cites.
Gundlach, C., “Nonspherical perturbations of critical collapse and cosmic censorship”, Phys. Rev. D
1999
Earlier work this paper cites.
Gundlach, C., “Critical gravitational collapse of a perfect fluid with p = k ρ p=k\rho : Nonspherical perturbations”, Phys. Rev. D
1999
Earlier work this paper cites.
Gundlach, C., and Martín-García, J.M., “Charge scaling and universality in critical collapse”, Phys. Rev. D
1999
Cited alongside, same era.
Gundlach, C., Price, R.H., and Pullin, J., “Late-time behavior of stellar collapse and explosions. II. Nonlinear evolution”, Phys. Rev. D
1999
Cited alongside, same era.
Hamadé, R.S., Horne, J.H., and Stewart, J.M., “Continuous self-similarity and S S -duality”, Class. Quant. Grav
1999
Cited alongside, same era.
Hamadé, R.S., and Stewart, J.M., “The spherically symmetric collapse of a massless scalar field”, Class. Quant. Grav
1999
Cited alongside, same era.
Hara, T., Koike, T., and Adachi, S., “Renormalization group and critical behavior in gravitational collapse”, (July, 1996). Related online version (cited on 10 December 1999): http://arXiv.org/abs/gr-qc/9607010
1999
Cited alongside, same era.
Husa, S., Lechner, C., Pürrer, M., Thornburg, J., and Aichelburg, P.C., “Type II critical collapse of a self-gravitating nonlinear σ \sigma -model”, Phys. Rev. D
2003
Later among the works it cites.
Husain, V., Kunstatter, G., Preston, B., and Birukou, M., “Anti-deSitter gravitational collapse”, Class. Quant. Grav
2003
Later among the works it cites.
Husain, V., and Olivier, M., “Scalar field collapse in three-dimensional AdS spacetime”, Class. Quant. Grav
2003
Later among the works it cites.
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
2003
Later among the works it cites.
Liebling, S.L., “The singularity threshold of the nonlinear sigma model using 3D adaptive mesh refinement”, Phys. Rev. D
2003
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Hirschmann, E.W., and Eardley, D.M., “Critical exponents and stability at the black hole threshold for a complex scalar field”, Phys. Rev. D
1999
Cited alongside, same era.
Hirschmann, E.W., and Eardley, D.M., “Universal scaling and echoing in gravitational collapse of a complex scalar field”, Phys. Rev. D
1999
Cited alongside, same era.
Hirschmann, E.W., and Eardley, D.M., “Criticality and bifurcation in the gravitational collapse of a self-coupled scalar field”, Phys. Rev. D
1999
Cited alongside, same era.
Hod, S., and Piran, T., “Critical behaviour and universality in gravitational collapse of a charged scalar field”, Phys. Rev. D
1999
Cited alongside, same era.
Hod, S., and Piran, T., “Fine-structure of Choptuik’s mass-scaling relation”, Phys. Rev. D
1999
Cited alongside, same era.
Horne, J., “Critical behavior in black hole collapse”, Matters of Gravity
1999
Cited alongside, same era.
Kiem, Y., “Phase transition in spherically symmetric gravitational collapse of a massless scalar field”, arxiv, (1994). Related online version (cited on 10 December 1999): http://arXiv.org/abs/hep-th/9407100
1999
Cited alongside, same era.
Liebling, S.L., Hirschmann, E.W., and Isenberg, J., “Critical phenomena in nonlinear sigma models”, J. Math. Phys
2003
Later among the works it cites.
Martín-García, J.M., and Gundlach, C., “Static and self-similar spherically symmetric solutions of the Einstein-Vlasov system”, Phys. Rev. D
2003
Later among the works it cites.
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
2003
Later among the works it cites.
Martín-García, J.M., and Gundlach, C., “Global structure of Choptuik’s critical solution in scalar field collapse”, Phys. Rev. D
2003
Later among the works it cites.
Novak, J., “Velocity-induced collapses of stable neutron stars”, Astron. Astrophys
2003
Later among the works it cites.
Olabarrieta, I., and Choptuik, M. W., “Critical phenomena at the threshold of black hole formation for collisionless matter in spherical symmetry”, Phys. Rev. D
2003
Later among the works it cites.
Peleg, Y., and Steif, A., “Phase transition for gravitationally collapsing dust shells in 2+1 dimensions”, Phys. Rev. D
2003
Later among the works it cites.
Pretorius, F., “Black hole mergers and unstable circular orbits”, Class. Quant. Grav
2003
Later among the works it cites.
Pretorius, F., and Choptuik, M.W., “Gravitational collapse in 2+1 dimensional AdS spacetime”, Phys. Rev. D
2003
Later among the works it cites.
Thornburg, J.and Lechner, C., Pürrer, M., Aichelburg, P.C., and Husa, S., “Episodic self-similarity in critical gravitational collapse”, in Proceedings of the 9th Marcel Grossman Meeting
2003
Later among the works it cites.
Wyman, M., “Static spherically symmetric scalar fields in general relativity”, Phys. Rev. D
2003
Later among the works it cites.
Petryk, R., Maxwell-Klein-Gordon fields in black hole spacetimes
2006
Later among the works it cites.
Aichelburg, P.C., Bizoń, P., and Tabor, Z., “Bifurcation and fine structure phenomena in critical collapse of a self-gravitating σ \sigma -field”, Class. Quant. Grav
2007
Closest in time.
Álvarez-Gaumé, L., Gómez, C., and Vázquez-Mozo, M.A., “Scaling Phenomena in Gravity from QCD”, Phys. Lett. B
2007
Closest in time.
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. Quant. Grav
2007
Closest in time.
Bizoń, P., “Equivariant self-similar wave maps from Minkowski spacetime into 3-sphere”, Commun. Math. Phys
2007
Closest in time.
Bizoń, P., Chmaj, T., Rostworowski, A., Schmidt, B.G., and Tabor, Z., “On vacuum gravitational collapse in nine dimensions”, Phys. Rev. D
2007
Closest in time.
Bizoń, P., Chmaj, T., and Schmidt, B.G., “Critical behavior in vacuum gravitational collapse in 4+1 dimensions”, Phys. Rev. Lett
2007
Closest in time.
Bizoń, P., Chmaj, T., and Schmidt, B.G., “Codimension-two critical behavior in vacuum gravitational collapse”, Phys. Rev. Lett
2007
Closest in time.
Bizoń, P., Szybka, S., and Wassermann, A., “Periodic self-similar wave maps coupled to gravity”, Phys. Rev. D
2007
Closest in time.
Bizoń, P., and Wassermann, A., “On the existence of self-similar spherically symmetric wave maps coupled to gravity”, Class. Quant. Grav
2007
Closest in time.
Bland, J., and Kunstatter, G., “The 5-D Choptuik critical exponent and holography”, (2007). Related online version (cited on 15 June 2007): http://arXiv.org/abs/hep-th/0702226
2007
Closest in time.
Bland, J., Preston, B., Becker, M., Kunstatter, G., and Husain, V., “Dimension-Dependence of the Critical Exponent in Spherically Symmetric Gravitational Collapse”, (2005). Related online version (cited on 15 June 2007): http://arXiv.org/abs/gr-qc/0507088
2007
Closest in time.
Burko, L.M., “Black hole singularities: a new critical phenomenon”, Phys. Rev. Lett
2007
Closest in time.
Cavaglià, M., Clément, G., and Fabbri, A., “Approximately self-similar critical collapse in 2+1 dimensions”, Phys. Rev. D
2007
Closest in time.
Caveny, S.A., and Matzner, R.A., “Adaptive event horizon tracking and critical phenomena in binary black hole coalescence”, Phys. Rev. D
2007
Closest in time.
Choptuik, M.W., Hirschmann, E.W., Liebling, S.L., and Pretorius, F., “Critical Collapse of the Massless Scalar Field in Axisymmetry”, Phys. Rev. D
2007
Closest in time.
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
2007
Closest in time.
Donninger, R., and Aichelburg, P.C., “A note on the eigenvalues for equivariant maps of the S U ( 2 ) SU(2) sigma-model”, (2006). Related online version (cited on 15 June 2007): http://arXiv.org/abs/math-ph/0601019
2007
Closest in time.
Donninger, R., and Aichelburg, P.C., “On the mode stability of a self-similar wave map”, (2007). Related online version (cited on 15 June 2007): http://arXiv.org/abs/math-ph/0702025
2007
Closest in time.
Frolov, A.V., “Self-Similar Collapse of Scalar Field in Higher Dimensions”, Class. Quant. Grav
2007
Closest in time.
Frolov, A.V., and Pen, Ue-Li, “The naked singularity in the global structure of critical collapse spacetimes”, Phys. Rev. D
2007
Closest in time.
Frolov, V.P., “Merger transitions in brane–black-hole systems: criticality, scaling and self-similarity”, Phys. Rev. D
2007
Closest in time.
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
2007
Closest in time.
Garfinkle, D., and Isenberg, J., “Numerical studies of the behavior of Ricci flow”, Contemporary Mathematics
2007
Closest in time.
Garfinkle, D., Mann, R., and Vuille, C., “Critical collapse of a massive vector field”, Phys. Rev. D
2007
Closest in time.
Gundlach, C., and Martín-García, J.M., “Kinematics of discretely self-similar spherically symmetric spacetimes”, Phys. Rev. D
2007
Closest in time.
Gundlach, C., and Martín-García, J.M., “Well-posedness of formulations of the Einstein equations with dynamical lapse and shift conditions”, Phys. Rev. D
2007
Closest in time.
Harada, T., Hideki, M., and Semelin, B., “Criticality and convergence in Newtonian collapse”, Phys. Rev. D
2007
Closest in time.
Jin, K.-J., and Suen, W.-M., “Critical Phenomena in Head-on Collisions of Neutron Stars”, Phys. Rev. Lett
2007
Closest in time.
Kol, B., “Choptuik Scaling and The Merger Transition”, (2005). Related online version (cited on 15 June 2007): http://arXiv.org/abs/hep-th/0502034
2007
Closest in time.
Lai, Chi-Wai, A Numerical Study of Boson Stars
2007
Closest in time.
2007
Closest in time.
Lechner, C., Staticity, self-similarity and critical phenomena in a self-gravitating nonlinear sigma model
2007
Closest in time.
Levin, J., “Gravity waves, chaos, and spinning compact binaries”, Phys. Rev. Lett
2007
Closest in time.
Millward, R.S., and Hirschmann, E.W., “Critical behavior of gravitating sphalerons”, Phys. Rev. D
2007
Closest in time.
Musco, I., Miller, J.C., and Rezzolla, L., “Computations of primordial black hole formation”, Class. Quant. Grav
2007
Closest in time.
Noble, S.C., A numerical study of relativistic fluid collapse
2007
Closest in time.
2007
Closest in time.
Oliveira-Neto, G., and Takakura, F.I., “Wyman’s solution, self-similarity and critical behaviour”, J. Math. Phys
2007
Closest in time.
Pürrer, M., Husa, S., and Aichelburg, P.C., “News from Critical Collapse: Bondi Mass, Tails and Quasinormal Modes”, Phys. Rev. D
2007
Closest in time.
Sarbach, O., and Lehner, L., “Critical bubbles and implications for critical black strings”, Phys. Rev. D
2007
Closest in time.
Snajdr, M., “Critical collapse of an ultrarelativistic fluid in the Γ → 1 \Gamma\to 1 limit”, Class. Quant. Grav
2007
Closest in time.
Sorkin, E., and Oren, Y., “On Choptuik’s scaling in higher dimensions”, Phys. Rev. D
2007
Closest in time.
Stevenson, R., The spherically symmetric collapse of collisionless matter. Exploring critical phenomena through finite volume methods
2007
Closest in time.
Szybka, S.J., “Chaotic self-similar wave maps coupled to gravity”, Phys. Rev. D
2007
Closest in time.
van Putten, M.H.P.M., “Approximate black holes for numerical relativity”, Phys. Rev. D
2007
Closest in time.
Ventrella, J.F., and Choptuik, M.W., “Critical Phenomena in the Einstein-Massless-Dirac System”, Phys. Rev. D
2007
Closest in time.
Wang, A., “Critical collapse of cylindrically symmetric scalar field in four-dimensional Einstein’s theory of gravity”, Phys. Rev. D
2007
Closest in time.