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];
Landsman a2101 [historical].
@ 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; & Cardoso et al, non-linear effects may not suffice
to save the strong cosmic censorship conjecture.
* 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.
@ 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];
Luna et al PRD(19)-a1810 [Einstein-Maxwell-scalar, spherical, numerical];
Hod IJMPD-a2012-GRF [compact proof].
@ 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);
> s.a. models for topology change.
@ 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];
Hod NPB(19)-a1801 [charged];
Rahman et al JHEP(19)-a1811 [higher-dimensional];
> s.a. 3D black holes [BTZ].
@ Quantum version: Caldarelli PRD(98) [toroidal quantum black holes];
Casadio et al PLB-a1503;
Emparan a2005-GRF;
> s.a. singularities in quantum gravity.
Violations, Counterexamples
> s.a. types of singularities [genericity of naked singularities].
* Idea: Counterexamples 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];
Dafermos & Luk a1710;
Cardoso et al PRL(18)
+ Reall Phy(18)
[indications of violation from perturbations of Reissner-Nordström-de Sitter black holes];
Cardoso et al PRD(18)-a1808,
Mo et al PRD(18)-a1808 [in charged black-hole spacetimes];
Goulart a1809 [in Einstein-Maxwell-dilaton theory];
Destounis PLB(19)-a1811 [with charged fermionic fields];
Andrade et al JHEP(19)-a1812 [higher-dimensional black hole collisions];
Fernandez a2007-PhD [semiclassical approach].
@ Violations of strong censorship:
Etesi a1905 [physical interpretation];
Destounis et al a2006;
Casals & Marinho a2006 [in rotating black holes];
Luna et al a2012.
@ Violations of weak censorship: Eperon et al a1906;
Andrade et al a2011 [in black-hole collisions].
@ In asymptotically AdS spacetimes: Niehoff et al CQG(16)-a1510 [and the superradiant instability of Kerr-AdS black holes];
Crisford & Santos PRL(17)-a1702
+ news sn(17)may [in 4D AdS];
Horowitz et al CQG(16)-a1604 [4D Einstein-Maxwell theory].
@ 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 of 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;
Horowitz & Santos a1901
[counterexamples removed if weak-gravity conjecture holds].
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];
Tavakoli et al PRD-a2012 [5D braneworld with Gauss-Bonnet term].
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