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-p_crit)^, where 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-in [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).
@ 2+1: Birmingham PRD(01)ht [BTZ and AdS-cft]; Cavaglià et al PRD(04)gq [ < 0 self-similar].
@ Higher-dimensional: Sorkin & Oren PRD(05)ht [massless scalar]; Bizon et al PRL(05) [4+1 vacuum]; Bland et al CQG(05)gq [scalar, dimension dependence of critical exponent]; Bizon et al PRL(06)gq [5D vacuum].
@ Dust: Singh & Joshi CQG(96); Joshi & Dwivedi CQG(99)gq/98 [spherical]; Olabarrieta gq/00-MSc.
@ 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 = k , nonspherical]; 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: Eardley et al PRD(95)gq [axion-dilaton]; Husa et al PRD(00)gq, Thornburg et al gq/00-MG9 [-model]; Ventrella & Choptuik PRD(03)gq [Dirac]; > 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 a0708-PhD [global vs local aspects].
@ Reviews: Bizón ACosm(96)gq; Choptuik gq/98-in; Brady & Cai gq/98-in; Gundlach ATMP(98)gq/97, LRR(99)gq/00, PRP(03)gq/02; Wang BJP(01)gq; Hortacsu gq/03-in; 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 gq/99-in [shells].

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