Cosmic Censorship Conjecture  

In General > s.a. black-hole formation; gravitational collapse.
* 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 has been found; Theoretical importance of black holes.
* Physical version: All singularities of gravitational collapse are hidden within black holes.
* Strong version (Penrose): The spacetime development of generic data is globally hyperbolic (no non-globally hyperbolic extensions allowed).
* Remark: Physical arguments may lead to conjecture even stronger versions.
@ Reviews: Clarke in(93), CQG(94); Wald gq/97-conf; Singh JAA(99)gq/98-proc; Królak PTPS(99)gq-proc; Joshi MPLA(02)gq-conf; Joshi a1010; Isenberg a1505-in [strong censorship].
@ Simple: Shapiro & Teukolsky AS(91).
@ General references: Kong et al EPJC(14)-a1310 [difficulty of carrying out tests]; Hamid et al CQG(14)-a1402 & CQG+ [role of the Weyl curvature].

Progress Toward a Proof or General Understanding
* Direct approach: Prove (i) Long-time existence theorem (e.g., using energy theorem), (ii) Non-extendibility; & Choquet, Chruściel, 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 93].
* Mechanism: The shear scalar plays a crucial role in determining the fate of a collapsing object; If the shear is sufficiently strong, it can conspire with inhomogeneities and delay the formation of trapped region so much that the geodesics can encounter a singularity before the apparent horizon forms.
@ Partial results: Giambò et al CQG(02)gq/01 [spherical case]; Rudnicki et al MPLA(06) [weak censorship]; Acquaviva et al a1508 [support from gravitational thermodynamics].
@ Mechanism: Joshi et al PRD(02)gq/01, PRD(04) [role of the shear scalar].

Specific Types of Spacetimes > s.a. causality violations; gowdy spacetime; Gravastar; modified theories; wormhole solutions.
@ General references: Chruściel & 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-proc; 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]; Mkenyeleye et al PRD(15)-a1503.
@ And topology change: Joshi & Saraykar PLA(87).
@ Black holes: Ford & Roman PRD(90) [black holes and moving mirrors]; Wagh & Maharaj GRG(99)gq [Vaidya-de Sitter]; Tóth GRG(12) [thought experiment on overcharging or overspinning a Kerr-Newman black hole]; Zimmerman et al PRD(13) [self-force as a cosmic censor]; Cardoso & Queimada GRG(15)-a1511 [spinning up black holes close to the Kerr solution].
@ Quantum version: Caldarelli PRD(98) [toroidal quantum black holes]; Casadio et al PLB-a1503; > s.a. singularities in quantum gravity.

Violations, Counterexamples > s.a. types of singularities [genericity of naked singularities].
* 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); Jacobson & Sotiriou JPCS(10)-a1006 [on overspinning or overcharging a black hole]; Barausse et al PRD(11)-a1106 [effect of radiation reaction and self-force]; Miyamoto et al PTEP(13)-a1108 [astrophysical censorship]; Niehoff et al a1510 [and the superradiant instability of Kerr-AdS black holes]; Crisford & Santos PRL(17) + news sn(17)may [in 4D AdS].
@ Inhomogeneous spherical dust: Mena et al PRD(00)gq [genericity].
@ With quantum particles: Matsas et al PRD(09)-a0905 [from particle tunneling]; Richartz & Saa PRD(11)-a1109 [scattering on spin-0 and spin-1/2 particles by a near-extreme Reissner-Nordström black hole]; Pappas AHEP(13)-a1312 [quantum considerations].
@ 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]; Etesi IJGMP(15)-a1503 [from exotic \({\mathbb R}^4\)s].
@ Critique of counterexamples: Unnikrishnan GRG(94), reply Joshi & Singh GRG(95); Brady et al PRL(98)gq [Cauchy horizon instability]; Hod PRL(08)-a0805; Barausse et al PRL(10) + news disc(10)dec.

Formulations and Variations > s.a. 2D gravity.
* Lorentz-violating theories: At least in some cases of spinning spacetimes a universal horizon forms between the outer and (would-be) inner horizons.
@ 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]; Etesi IJTP(13)-a1205 [strong, proof of the Geroch-Horowitz-Penrose formulation].
@ 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]; Ortín FdP(07)ht/06 [unbroken supersymmetry excludes most naked singularities]; Meiers et al PRD(16)-a1511 [Lorentz-violating theories].


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