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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