Spacetime Singularities| 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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