Spacetime Singularities  

In General > s.a. singularity theorems.
* Idea: A spacetime is said to be non-singular if it is timelike and null geodesically complete, by analogy with Riemannian geometry, where geodesic completeness is equivalent to the usual metric completeness.
* Remark: When this condition is violated we may not have what we would like to call a singularity physically; And, when satisfied, we might have, e.g., timelike lines of finite acceleration which are incomplete.
* Consequences: Naked singularities would be a problem for predictive physics.

Avoiding Singularities > s.a. early-universe models; singularities in quantum gravity.
* History: An attempt was made by the Soviets with the mixmaster universe; Other possibilities include cosmic censorship, violation of energy conditions, "gravastars", perhaps quantum gravity (non-commutative? > see Kasner Solutions), and varying physical constants.
@ General references: Einstein & Rosen BB(31), PR(35); Einstein AM(39), AM(45); Einstein & Straus AM(46); in Misner et al 73.
@ By violating energy conditions: Fulling & Parker PRD(73) [quantum]; Bekenstein PRD(75) [classical]; Fakir gq/98.
@ By going to a different metric: Quirós PRD(00)gq/99, et al PRD(00) [geometric duality in general relativity and Brans-Dicke theory]; Quirós gq/00, et al gq/00/PRD [conformal rescaling]; Wetterich a2004 [requires tuning of parameters]; Casadio et al a2008 [no singularities in pure gravity].
@ By extending the spacetime: Śniatycki in(91) [using the Jacobi metric]; Deruelle & Sasaki PTPS(11)-a1012-proc [conformal transformations in Nordström's scalar theory]; Stoica CTP(12)-a1203, CEJP(14)-a1203, PhD(13)-a1301 [new field equation applicable in wider situations]; Heller & Król a1711 [beyond the boundary, using Synthetic Differential Geometry]; Nomura & Yoshida a2105 [FLRW and Bianchi I spacetimes]; > s.a. lorentzian geometry; metric matching [junction conditions]; FLRW geometry; schwarzschild spacetime.
@ In different theories: Mac Conamhna CMP(08)-a0708 [M-theory]; Dąbrowski & Marosek JCAP(13)-a1207, Dąbrowski et al a1308-proc [varying constants]; Garattini & Majumder NPB(14)-a1311 [Gravity's Rainbow and non-commutative geometry]; Bambi et al PLB(14)-a1402 [from four-fermion interaction]; Tahamtan & Svítek EPJC(14)-a1312 [and quantum gravity]; Bazeia et al PRD(15)-a1507 [higher-dimensional metric-affine theories]; Koslowski et al PLB(18)-a1607 [relational degrees of freedom]; Chamseddine & Mukhanov JCAP(17)-a1612 [modified longitudinal mode]; Edholm & Conroy PRD(17)-a1710 [infinite-derivative gravity]; > s.a. Relational Theories.
@ Related topics: Heller & Sasin IJTP(95), GRG(99)gq/98 [algebraically]; Raptis IJTP(06)gq/04 [Schwarzschild, finitary-algebraic]; Goswami & Joshi gq/05 [by not forming trapped surface]; Gershtein et al TMP(05)gq [in field theory of gravitation?]; Qiu CQG(10)-a1007 [by coupling gravity to a scalar field]; > s.a. modified electromagnetic theory; non-commutative gravity; types of singularities [evolving through the cosmological singularity].

Other References > s.a. collapse [including Hoop conjecture]; cosmic censorship; cosmology and models; types of singularities; spacetime boundary.
@ Reviews: Canarutto RNC(88); Clarke in(88); Rendall in(05)gq; Cotsakis & Klaoudatou JPCS(05); Natário m.DG/06 [introduction for mathematicians]; Cotsakis gq/07-MGXI; Joshi & Malafarina IJMPD(11)-a1201 [collapse and phenomenology]; Joshi a1311-ch; Dąbrowski a1407-in [rev, different types, avoidance]; Hawking EPJH(14) [intro]; Ong IJMPA-a2005 [and censorship].
@ History: Khalatnikov & Kamenshchik PU(08)-a0803, Belinski IJMPD(14)-a1404 [cosmological]; Senovilla & Garfinkle CQG(15)-a1410 [Penrose's 1965 theorem].
@ Philosophical: Earman 95; Lam PhSc(07)dec.
@ General references: Geroch JMP(68), in(68); Hájíček GRG(70); Newman GRG(71); Penrose in(78); Barrow & Tipler PRP(79), PLA(81); Fuchs et al FdP(88); Joshi SA(09)feb [naked singularities]; Stoica a1207-talk; Romero FS-a1210 [ontology, against the physical existence of singularities]; Cotsakis IJMPD(13)-a1212 [and asymptotics]; Uggla a1304-conf, IJMPD(13)-a1306-MG13 [spacelike singularities]; Tavakoli PhD(13)-a1405; Stoica a1504 [and causal structure].
@ And initial surfaces: Wojtkiewicz PRD(90).
@ Data at singularities: Eardley et al JMP(72); Tod CQG(90); & Goode & Wainwright.
@ Matter at singularities: Stoica a1408-conf [gauge fields].
@ Strength and physical properties: Kánnár & Rácz JMP(92); Kánnár GRG(95) [in Einstein-Cartan theory]; Kriele & Lim CQG(95); Ori PRD(00); > s.a. wormhole solutions [curvature divergences and physical observers].
@ Role, uses of singularities: Earman FP(96); Lopez CQG(93); Horowitz & Myers GRG(95)gq; Azhar & Namjoo a2101 [and indeterminism].
@ Probing singularities: Horowitz & Marolf PRD(95)gq; Ishibashi & Hosoya PRD(99)gq; Piechocki PLB(02); Konkowski et al in(03)gq/04 [quantum particles]; Blau et al JHEP(06)ht [with scalar fields]; Pitelli & Letelier IJMPD(11)-a1010 [with quantum wave packets, static spacetimes]; Hofmann & Schneider PRD(17)-a1611 [Schwarzschild black holes].
@ In f(R) gravity: Lee et al PTP(12)-a1201; Tahamtan & Gurtug EPJC(12)-a1205 [with quantum test fields as probes].
@ In other theories of gravity: Eguchi MPLA(92) [topological field theories]; Novello et al CQG(00) [general relativity + non-linear electrodynamics]; Holdom PRD(02) [spherical, and horizons]; Ferraz Figueiro & Saa PRD(09)-a0906 [modified-gravity models]; Konkowski & Helliwell IJMPA(11)-a1112 [quantum singularities]; > s.a. Bakry-Emery Tensor; cosmology in higher-order gravity; hořava-lifshitz gravity phenomenology; massive gravity; singularity theorems; types of singularities [naked singularities].

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