Cosmic Censorship Conjecture

In General > s.a. gowdy spacetime.
* Idea: Naked singularities form with zero probability in the gravitational collapse of astrophysical objects.
* Motivation: Linearized Schwarzschild and Kerr give non-singular exteriors; No non-highly-symmetric counterexample found; theoretical importance of black holes.
* Physical: All singularities of gravitational collapse are hidden within black holes.
* Strong (Penrose): The spacetime development of generic data is globally hyperbolic (no non-globally hypoerbolic extensions allowed).
* Remark: Physical arguments may lead to conjecture even stronger versions.

Progress Toward a Proof
* Direct approach: Prove (i) Long-time existence theorem (e.g., using energy theorem), (ii) Non-extendibility; & Choquet, Chrusciel, Isenberg, Moncrief.
* Numerical approach: & B Berger.
* Perturbative analytical approach: Multiple scale methods; gives indications that polarized Gowdy is velocity-dominated; & Grubisic.
* Special cases: Something, but not much, is known for U(1) symmetry (1995).
* General case: 1995, Only stability of Minkowski known [@ Christodoulou & Kleinerman].
@ Partial results: Giambò et al CQG(02)gq/01 [spherical case]; Rudnicki et al MPLA(06) [weak censorship].

Specific Types of Spacetimes > s.a. causality violations; Gravastar; modified theories; types of singularities.
@ General references: Chrusciel & Rendall AP(95)gq/94; Rendall AP(94); Malec CQG(96); Horowitz & Sheinblatt PRD(97) [Ernst spacetime]; Caldarelli PRD(98) [toroidal quantum black holes]; Dafermos & Rendall gq/06 [T²-symmetric cosmologies with collisionless matter].
@ Collapse: Rudnicki PLA(96), Rudnicki & Zieba PLA(00) [Kerr-like]; Singh gq/96-in; Deshingkar et al GRG(98)gq [Szekeres, quasi-spherical dust]; Barve et al CQG(99)gq [dust]; Christodoulou AM(99) [scalar field]; Ghosh IJMPD(05) [dust, in de Sitter].
@ Collapse, higher-dimensional: Ghosh & Saraykar PRD(00)gq/01 [radiation]; Goswami & Joshi PRD(04)gq/02 [spherical]; Goswami & Joshi PRD(04)gq, Mahajan et al PRD(05)gq [dust, removal of singularities]; Yoo et al PRD(05)gq [5D, counterexample?]; Patil & Zade IJMPD(06) [spherical].
@ And topology change: Joshi & Saraykar PLA(87).
@ Related topics: Ford & Roman PRD(90) [black holes and moving mirrors]; Wagh & Maharaj GRG(99)gq [Vaidya-de Sitter].

Violations, Counterexamples
* Idea: Can be obtained with perfect fluids, as well as marginal ones with a scalar field; But must impose regularity conditions on the matter and look at realistic non-symmetric situations to avoid spurious violations.
@ General references: Yodzis et al CMP(73), CMP(74) [perfect fluid]; Roberts GRG(89), Christodoulou AM(94) [scalar field]; Husain GRG(98).
@ Inhomogeneous spherical dust: Mena et al PRD(00)gq [genericity].
@ In quantum theory: Matsas et al PRD(09)-a0905 [from particle tunneling].
@ Generic violation? Hertog et al PRL(04)gq/03 [proposal], gq/04 ["gap"]; Alcubierre et al gq/04 [loophole], gq/04 [argument review]; Garfinkle PRD(04)gq, PRD(04)gq [simulation].
@ Critique of counterexamples: Unnikrishnan GRG(94), reply Joshi & Singh GRG(95); Brady et al PRL(98)gq [Cauchy horizon instability]; Hod PRL(08)-a0805.

References > s.a. 2D gravity; collapse; quantum-gravity phenomenology.
@ Reviews: Clarke in(93), CQG(94); Wald gq/97-in; Singh gq/98-in; Królak PTPS(99)gq-in; Joshi gq/02-in.
@ Simple: Shapiro & Teukolsky AS(91).
@ Proposals, formulations: Penrose RNC(69); Israel FP(74); Królak CQG(86), JMP(87); Wagh gq/02; Etesi PLB(02) [strong censorship and computability]; Santiago-Germán gq/05 [strong].
@ String-inspired: Maeda et al PRL(98)gq; Gutperle & Kraus JHEP(04)ht, Frolov PRD(04)ht [numerical].
@ In other theories: Vaz & Witten CQG(96)gq/95 [2D dilaton gravity]; Nakao et al PLB(03) [brane world]; Ortin FdP(07)ht/06 [unbroken supersymmetry excludes most naked singularities].

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