Criticality and Self-Similarity in Gravitational Collapse  

In General > s.a. 3D gravity; causality violation; singularities; solutions with symmetries.
* The issue: M Choptuik, in numerical simulations of spherically symmetric scalar field collapse, found that, near the threshold for black-hole formation (criticality), the mass of the black hole that forms always depends on the parameter p in a family of initial data as ∝ (p-pcrit)γ, where γ is the same for all kinds of matter and initial conditions (universality); The critical solution depended on r and t only through the combination r/t (self-similarity).
* Development: Many other studies, with different families of data and types of matter, numerical and to some extent analytical, done since the first one; Universality may not be true [@ Maison PLB(96)gq/95].

Types of Matter and Theories > s.a. 3D black holes.
@ Scalar: Hirschmann & Eardley PRD(95), PRD(95)gq [complex], PRD(97)gq/95 [sigma model]; Gundlach PRD(97)gq/96 [massless]; Hamadé & Stewart CQG(96)gq/95 [massless]; Brady PRD(95), et al PRD(97)gq, Chambers et al gq/97-MG8 [massive, spherical]; Hod & Piran PRD(97) [charged]; Frolov PRD(00)gq/99 [continuous to discrete self-similar]; Martín-García & Gundlach PRD(03) [global structure]; Hirschmann et al CQG(04)gq/02 [2+1]; Choptuik et al PRL(04)gq [complex, with angular momentum].
@ 2+1, scalar + cosmological constant: Pretorius & Choptuik PRD(00) [numerical]; Husain & Olivier CQG(01); Garfinkle PRD(01) [exact]; Clément & Fabbri CQG(01), NPB(02); Jałmużna et al a1510 [massless, numerical].
@ 2+1: Birmingham PRD(01)ht [BTZ and AdS-cft]; Cavaglià et al PRD(04)gq [Λ < 0 self-similar].
@ Higher-dimensional: Sorkin & Oren PRD(05)ht [massless scalar]; Bizoń et al PRL(05) [4+1 vacuum]; Bland et al CQG(05)gq [scalar, dimension dependence of critical exponent]; Bizoń et al PRL(06)gq [5D vacuum]; Taves & Kunstatter PRD(11)-a1105 [in Painlevé-Gullstrand coordinates].
@ Dust: Singh & Joshi CQG(96); Joshi & Dwivedi CQG(99)gq/98 [spherical]; Olabarrieta MSc(00)gq.
@ Fluids: Maison PLB(96)gq/95 [non-universality]; Neilsen & Choptuik CQG(00)gq/98; Koike et al PRD(99); Carr e al PRD(00)gq/99, CQG(01)gq/99; Gundlach PRD(02)gq/99 [p = , non-spherical]; Harada & Maeda PRD(01)gq [spherical]; Gundlach PRD(02)gq/01 [rotating].
@ Einstein-Yang-Mills: Choptuik et al PRL(96)gq, PRD(99)gq; Gundlach PRD(97)gq/96 [echoing and scaling].
@ Newtonian gravity: Maeda & Harada PRD(01)gq; Harada et al PRD(03)gq/02.
@ Other fields and theories: Eardley et al PRD(95)gq [axion-dilaton]; Husa et al PRD(00)gq, Thornburg et al gq/00-MG9 [σ-model]; Ventrella & Choptuik PRD(03)gq [Dirac]; Golod & Piran PRD(12)-a1201 [Einstein-Gauss-Bonnet gravity]; > s.a. Sphaleron.

References > s.a. solar system.
@ General: Choptuik PRL(93); Abrahams & Evans GRG(94); Aquilano et al GRG(94); Husain et al PRD(94); Das et al JMP(95); Pürrer PhD(07)-a0708 [global vs local aspects]; Reiterer & Trubowitz a1203 [existence of an analytic solution].
@ Reviews: Bizoń ACosm(96)gq; Choptuik gq/98-GR15; Brady & Cai gq/98-MG8; Gundlach ATMP(98)gq/97, LRR(99)gq/00, PRP(03)gq/02; Wang BJP(01)gq; Hortacsu gq/03-conf; Gundlach & Martín-García LRR(07)-a0711.
@ Formulations: Garfinkle PRD(95)gq/94 [null]; Gundlach PRL(95)gq [eigenvalue problem]; de Oliveira & Soares IJMPA(02) [dynamical system]; > s.a. einstein's equation.
@ Renormalization approach: Hara et al gq/96; Iguchi et al PRD(98)gq/97.
@ Self-similarity, scale invariance: Garfinkle & Meyer PRD(99); Lechner et al PRD(02) [discrete/continuous bifurcation, sigma model].
@ Analytical models: Koike & Mishima PRD(95); Husain et al CQG(96)gq/95; Price & Pullin PRD(96)gq [approximations]; Wang PRD(03)gq [cylindrical Klein-Gordon]; Mahajan & Joshi GRG(07)gq/05.
@ Perturbations: Frolov PRD(97)gq, PRD(99)gq/98; Gundlach PRD(98)gq/97 [non-spherical]; Garfinkle et al PRD(99)gq/98 [angular momentum]; Martín-García & Gundlach PRD(99)gq/98 [non-spherical]; Garfinkle & Gundlach PRD(02)gq [2+1 + scalar].
@ Related topics: Evans & Coleman PRL(94) [radiation]; Pullin PLA(95)gq/94 [and no-hair]; Gundlach PRD(98)gq/97 [angular momentum behavior]; Pürrer et al PRD(05)gq/04 [radiation and news].
@ Quantum: Strominger & Thorlacius PRL(94); Tomimatsu PRD(95); Brady & Ottewill PRD(98)gq; Casadio NPPS(00)gq/99 [shells]; Husain ASL(09)-a0808.


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