Types of Spacetime Singularities  

In General
* Criteria: The divergence of a curvature scalar can be used to find some singularities, but some are not curvature singularities; A more general criterion is the existence of incomplete geodesics (usually timelike or null) in the spacetime.
* Types: Isolated objects (black holes, white holes, naked singularities), cosmological singularities (can be spatially homogeneous, velocity-dominated or mixmaster-like).
* Tools: Global techniques in Lorentzian geometry, using properties of congruences of geodesics and assumptions on the curvature (usually the weak or strong energy conditions); 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.
* 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).

Naked Singularities > s.a. censorship; gravitational collapse; scalar-tensor theories.
@ 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-MG8; Kudoh et al PRD(00) [HIN spacetime]; Joshi et al PRD(02)gq/01, PRD(04) [shearing effects]; Giambò & Magli DG&A(03)mp/02 [dust], et al CQG(03)gq/02, CQG(03) [conditions]; Dafermos ATMP(05)gq/04 [spherical, scalar]; Harada Pra(04)gq-in; Mitsuda et al PRD(05)gq [electromagnetic radiation]; Ziaie et al GRG(11)-a1106 [in f(R) gravity]; Ortiz AIP(12)-a1204 [spherically symmetric dust collapse].
@ Lower-dimensional: Oliveira-Neto IJMPD(03)gq/02 [2+1]; García-Islas a1511 [2D model].
@ Higher-dimensional: Debnath et al GRG(04)gq/03, Debnath & Chakraborty JCAP(04)mp/03, GRG(05)gq/03 [Szekeres spacetime, dust]; Langfelder & Mann CQG(05)gq/04 [spherical, any D]; An & Zhang AHP(18)-a1509.
@ Negative mass: Gibbons et al PTP(05)ht/04 [Schwarzschild, stability]; Cardoso & Cavaglià PRD(06)gq [4D Schwarzschild, -dS/-AdS, instability].
@ Vs black holes: Joshi et al CQG(13)-a1304 [accretion disk properties]; Ortiz et al CQG(15)-a1401; > s.a. black-hole mimickers; lensing.
@ Appearance, phenomenology: Schiffer GRG(93); Dwivedi PRD(98); Joshi PRD(07); Deshingkar IJMPD(09)-a0710; Deshingkar a1012 [unobservability of null naked singularities]; Sahu et al PRD(12)-a1206 [and strong gravitational lensing]; Maluf GRG(14)-a1401 [repulsive force]; Boshkayev et al PRD(16)-a1509 [test particles]; Dey et al IJMPD(19)-a2101 [at the galactic center, test]; > s.a. sources of gravitational radiation.
@ Behavior of null geodesics: Nakao et al PRD(03)gq/02; Dadhich & Zaslavskii IJMPD(09)-a0811.
@ Behavior of quantum fields: Iguchi & Harada CQG(01)gq; Batic et al EPJC(11)-a1005 [Dirac equation, repulsive nature of singularity].
@ Related topics: Vaz & Witten PLB(98) [radiation spectrum]; Brax & Davis PLB(01) [branes]; Miyamoto et al PTP(05)gq/04 [quantum effects]; Dotti et al PLB(07)gq/06 [instability]; Joshi Pra(07)gq-in, Joshi & Malafarina GRG(13)-a1105 [genericity]; Sadhu & Suneeta IJMPD(13)-a1208 [stability under scalar field perturbations]; Stuchlík et al EPJC(15)-a1412 [perfect fluid tori orbiting Kehagias-Sfetsos naked singularities]; Manko & Ruiz PLB(19)-a1803 [black hole and naked singularity dualism]; Rodnianski & Shlapentokh-Rothman a1912 [exterior region]; Hernandez-Lorenzo & Steinwachs a2003 [in quadratic f(R) gravity]; > s.a. Antigravity; types of geodesics.

Specific Types of Spacetimes > s.a. black holes and information [endpoint of evaporation]; cosmological singularities; Levi-Civita Spacetime.
@ 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]; Krasiński & Bolejko PRD(06) [charged dust, singularity avoidance]; Fayos & Torres CQG(11)-a1204, CQG(12)-a1204 [invariant causal characterization]; > s.a. schwarzschild solution.
@ Inside black holes: Ori PRL(92), PRL(99) [oscillatory]; Burko PRD(99)gq; Gorbonos & Wolansky JMP(07)gq/06 [mathematical model]; Stoica AHEP(14)-a1401 [geometry]; Chakraborty et al PRD(17)-a1605 [Kerr spacetimes]; > s.a. particles in kerr spacetimes [overspinning].
@ Critical collapse: Burko PRL(03)gq/02; Frolov & Pen PRD(03)gq.

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; They 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.
@ Velocity-dominated: Eardley et al JMP(72); Demaret et al PLB(85); Choquet-Bruhat & Isenberg JGP(06)gq/05 [half-polarized].
@ 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]; > s.a. cosmological models.
@ 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]; Wilson CQG(00)gq [hyperbolicity]; Kenmoku et al IJMPD(03) [3D, ADM formalism]; Hörmann a1501 [and global hyperbolicity]; > s.a. gravitational energy; topological defects; holonomy; scattering; types of lorentzian geometries.
@ Spacelike: Sandin & Uggla CQG(10)-a0908 [and perfect fluid properties]; Uggla GRG(13).
@ 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]; Bray & Jáuregui AJM-a0909 [zero-area singularities]; Konkowski & Helliwell a1006-MG12; Lukash & Strokov IJMPA(13)-a1301 [integrable singularity]; Luk JAMS(18)-a1311 [weak null singularities]; > s.a. gravitational-wave solutions [impulsive]; metric types [degenerate]; spacetime boundaries.

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