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].

@ __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]; > 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 a1607
[relational degrees of freedom]; Chamseddine & Mukhanov a1612 [modified longitudinal mode].

@ __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);
Senovilla GRG(98);
Cotsakis LNP(02)gq
[in cosmology]; Rendall in(05)gq;
Natário m.DG/06
[introduction for mathematicians]; Senovilla phy/06-conf;
Cotsakis gq/07-MGXI;
Joshi & Malafarina IJMPD(11)-a1201
[collapse and phenomenology]; Joshi a1311-ch;
Dąbrowski a1407-in
[rev, different types, avoidance].

@ __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.

@ __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 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].

@

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