Types of Spacetime Singularities  

In General
* From global causality: Black holes, white holes, naked singularities.
* Tools: Bundle of linear frames over spacetime [@ Hawking & Ellis 73, #8.3]; Cauchy-Kowalewska method, to produce spacetimes with Cauchy horizons, then Geroch transfomations to singular ones.
* Spatially homogeneous: Singularities can be velocity-dominated or mixmaster-like.
* Results: Indications that either the Cauchy horizon has closed generators and a Killing vector field, or, if compact, it has 2 commuting Killing vector fields (& Isenberg & Marsden).

Approach to Singularity > s.a. bianchi models; chaos in bianchi models; quantum gravity phenomenology.
* BKL conjecture: In spatially inhomogeneous cosmologies, collapse is dominated by local Kasner or Mixmaster behavior.
@ General references: Lifshitz & Khalatnikov AiP(63); Belinskii & Khalatnikov JETP(69), et al AiP(70), AiP(82) [singularity in time]; Nolan CQG(01)gq [isotropic]; Deshingkar et al PRD(02)gq/01 [spherical]; Garfinkle PRL(04)gq/03 [numerical]; Khalatnikov et al JCAP(03) [2-fluid]; Garfinkle IJMPD(04)gq-GRF; Andersson et al PRL(05)gq/04 [asymptotic silence]; Heinzle et al gq/07 [billiard attractor]; Damour & de Buyl a0710 [using Iwasawa variables].
@ Inhomogeneous: Montani CQG(95); Berger gq/98-in; Berger et al MPLA(98)gq; Weaver et al PRL(98); Berger gq/01-in.
@ 2-torus symmetry: Weaver et al gq/01-MG9; Berger et al PRD(01)gq.
@ U(1) symmetry: Berger & Moncrief PRD(98)gq [polarized], PRD(98) [generic]; Isenberg & Moncrief CQG(02)gq [vacuum]; Berger CQG(04)gq/03.
@ Other types: Parnovsky CQG(90) [timelike]; Andersson & Rendall CMP(01)gq/00 [quiescent].
@ Various theories: Berger PRD(00)gq/99 [with scalar field]; Damour et al CQG(03)ht/02 [Einstein-dilaton-p-form]; Benini et al CQG(05)gq [higher dimensions].

Naked Singularities > s.a. censorship; collapse; lensing; sources of gravitational radiation; scalar-tensor.
@ Spherical: Weitkamp JGP(05) [existence]; Giambò JMP(06)gq [visibility]; > s.a. spherical solutions.
@ Other types: Newman & Joshi AP(88) [close to spherical]; Virbhadra gq/96 [exact directional asymptotically flat solution]; Maeda et al PRL(98) [string-inspired theory].
@ And collapse: Shapiro & Teukolsky PRL(91); Joshi & Dwivedi CMP(92), LMP(93); Jhingan gq/97-in; Kudoh et al PRD(00) [HIN spacetime]; Joshi et al PRD(02)gq/01 [shearing effects]; Oliveira-Neto IJMPD(03)gq/02 [2+1]; Giambò & Magli DG&A(03)mp/02 [dust], et al CQG(03)gq/02, CQG(03) [conditions]; Debnath et al GRG(04)gq/03, Debnath & Chakraborty JCAP(04)mp/03, GRG(05)gq/03 [higher-D Szekeres, dust]; Dafermos ATMP(05)gq/04 [spherical, scalar]; Harada gq/04-in; Langfelder & Mann CQG(05)gq/04 [spherical, any D]; Mitsuda et al PRD(05)gq [em radiation].
@ Negative mass: Gibbons et al PTP(05)ht/04 [Schwarzschild, stability]; Cardoso & Cavaglià PRD(06)gq [4D Schw, -dS/-AdS, instability].
@ Visibility, appearance: Schiffer GRG(93); Dwivedi PRD(98); Joshi PRD(07); Deshingkar a0710.
@ Related topics: Vaz & Witten PLB(98) [radiation spectrum]; Brax & Davis PLB(01) [branes]; Iguchi & Harada CQG(01)gq [behavior of quantum fields]; Nakao et al PRD(03)gq/02 [behavior of null geodesics]; Miyamoto et al PTP(05)gq/04 [quantum effects]; Dotti et al PLB(07)gq/06 [instability]; Joshi gq/07-in [genericity].

Specific Types of Spacetimes > s.a. black holes and information [endpoint of evaporation]; branes; gowdy; Levi-Civita.
@ Spherical symmetry: Guven & O'Murchadha PRD(97)gq; Silaev & Turyshev GRG(97) [axial stability]; Deshingkar et al PRD(99) [collapse]; Nolan PRD(99)gq [strength]; Singh CQG(99) [collapse, shell-focusing]; Barve et al CQG(99), Nolan & Mena CQG(02)gq [dust]; Krasinski & Bolejko PRD(06) [charged dust, singularity avoidance]; > s.a. schwarzschild.
@ Cosmological: Ove PRD(89) [expanding spacetimes]; Lake CQG(04), Barrow CQG(04)gq, Fernández-Jambrina & Lazkoz PRD(04)gq [sudden, future]; Tchapnda CQG(04) [Einstein-Vlasov-cosmological constant]; Kotsakis & Klaoudatou gq/05-in [rev], JGP(05) [future]; Cotsakis & Klaoudatou JGP(07)gq/06 [and Bel-Robinson energy]; Cotsakis gq/06-in [future]; Malkiewicz & Piechocki CQG(06) [quantum particle as probe]; Dabrowski & Balcerzak gq/07-in; Uggla a0706-in; Khalatnikov & Kamenshchik a0803-PU [history]; > s.a. frw models.
@ Cosmological, FRW milestones: Cattoen & Visser CQG(05)gq, gq/06-in; Cattoen gq/06-MSc; Cattoen & Visser gq/06-in [behavior].
@ Cosmological, string-inspired: Larsen & Wilczek PRD(97), Cornalba et al NPB(02) [resolution]; Liu et al gq/03; Sánchez IJMPA(03)ht.
@ Bianchi models: Collins & Ellis PRP(79); De Rop GRG(89) [VI & VII]; Rendall CQG(97)gq; Ringström AIHP(01)gq/00 [IX]; Abramo et al IJTP(03)gq, PRD(03) [non-minimal scalar]; Montani et al a0712-IJMPA [IX, classical and quantum]; > s.a. Silent Universes.
@ Inhomogeneous: Rendall GRG(95)gq/94 [plane symmetry with scalar field], gq/98-in; Berger & Moncrief PRD(00)gq, PRD(00)gq [U(1) symmetry].

Other Kinds of Singularities > s.a. 3D quantum gravity; numerical relativity models; singularities [other theories]; wave phenomena.
* Conformal singularities: They are transformed into a regular spacelike hypersurface by a conformal transformation.
* Quasiregular: The mildest true classical type of singularity; Can include disclinations and dislocations.
* Generalized hyperbolicity: Analogous to global hyperbolicity, but based on behavior of test fields.
* Quantum mechanically singular: One in which the spatial derivative operator for a field equation is not essentially self-adjoint.
@ Inside black holes: Ori PRL(92), PRL(99) [oscillatory]; Burko PRD(99)gq; Gorbonos & Wolansky gq/06 [mathematical model].
@ Critical collapse: Burko PRL(03)gq/02; Frolov & Pen PRD(03)gq.
@ Velocity-dominated: Eardley et al JMP(72); Demaret et al PLB(85); Choquet-Bruhat & Isenberg JGP(06)gq/05 [half-polarized].
@ Isotropic: Goode & Wainwright CQG(85); Tod CQG(90); Goode et al CQG(92); Scott & Ericksson gq/98-in; Ericksson & Scott GRG(00)gq/01 [shear-free], GRG(02)gq/03 [and matter]; Anguige & Tod AP(99)gq, AP(99)gq; Anguige AP(00)gq/99; Klaoudatou & Cotsakis gq/06-in [and Bel-Robinson energy]; Barrow & Middleton gq/07 [in quadratic gravity, stable]; Tod CQG(07)-a0705 [with cosmological constant].
@ Quasiregular: Ellis & Schmidt GRG(77); Konkowski et al PRD(85), Konkowski & Helliwell PRD(85) [in cosmology]; Puntigam & Soleng CQG(97) [dislocations]; Helliwell et al GRG(03) [quantum field theories as probes].
@ C0: Nolan gq/99; Ori gq/99, PRD(00).
@ Strong: Rudnicki & Zieba PLA(00), Rudnicki et al MPLA(02) [and censorship].
@ Conical: Tod CQG(94); Oliveira-Neto JMP(96); Maluf & Kneip JMP(97)gq/95 [energy]; Dahia & Romero MPLA(99)gq/98 [curvature]; Wilson CQG(00)gq [hyperbolicity]; Kenmoku et al IJMPD(03) [3D, ADM formalism]; > s.a. gravitational energy, topological defects, holonomy, scattering.
@ Other types: Newman PRS(93), PRS(93) [conformal]; Rendall CQG(95)gq/94 [crushing]; Ori & Flanagan PRD(96)gq/95 [null]; Clarke CQG(98)gq/97 [generalized hyperbolicity]; > s.a. bianchi models [whimper]; metric types [degenerate].

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