Gravity Theories with Extended Metric Signatures  

In General
* Idea: Some extended theories of gravity admit non-Lorentzian metric signatures (e.g., Riemannian or degenerate metrics), at least at some points of the spacetime manifold (e.g., extended regions replacing the cosmological singularity or isolated points), or admit complex metrics.

Degenerate Metrics
* Idea: Use variables (typically including connections) whose inverse does not appear in the equations.
@ References: Jacobson & Romano CQG(92)gq; Canarutto JMP(98) [degenerate tetrads + Maxwell-Dirac fields]; Kaul & Sengupta PRD(16)-a1609 [tetrads], PRD(17)-a1709 [degenerate extension of the Schwarzschild exterior]; Kaul CQG(19)-a1803 [first-order gravity with matter].
> Related topics: see geometrodynamics; models of topology change.
> Examples, applications: see early-universe models; models in canonical general relativity; types of metrics and singularities.

Signature Change > s.a. lorentzian geometries [type-changing metrics].
* Motivation: Problems in causality implied by isotropy and homogeneity, and quantum cosmology and the initial singularity.
@ Precursor: Sakharov JETP(84)/SPU(91).
@ General references: Dray et al GRG(91); Ellis GRG(92), et al CQG(92); Dereli & Tucker CQG(93); Ellis in(93); Hayward gq/93; Kossowski & Kriele CQG(93), CQG(93), comment Dray & Hellaby GRG(96)gq; Hellaby & Dray PRD(94)gq; Carfora & Ellis IJMPD(95)gq/94; Ellis & Piotrkowska IJMPD(94); Kossowski & Kriele PRS(94); Kriele CQG(94); Hayward gq/96, PRD(95)gq/96; Dray et al GRG(97)gq/96, GRG(01)gq/00 [Colombeau theory]; Iliev PS(02)gq/98 [metric connection]; Stewart CQG(01) [well-posed problems]; Borowiec et al IJGMP(07) [Lagrangian formalism]; Otway JGP(08); Zhang PRD(19)-a1909 [alternative route].
@ Matter fields: Dray et al PRD(93)gq [scalar]; Romano PRD(93)gq [scalar + spinor]; Dray et al CQG(95)gq [scalar], comment Hayward gq/95; Ghafoori-Tabrizi et al IJMPA(00)gq/99, Vakili & Jalalzadeh PLB(13)-a1308 [FLRW model with scalar]; > s.a. generalized quantum field theories.
@ Distributional approach: Hartley et al GRG(00)gq/97; Mansouri & Nozari GRG(00); Steinbauer mp/01-proc; > s.a. distributions.
@ Applications: Hayward CQG(92), CQG(93) [cosmology]; Embacher PRD(95)gq/94, CQG(95)gq/94 [compactification].
@ Related topics: Hosoya & Ding CQG(93) [2+1]; Hayward CQG(94) [weak solutions]; Egusquiza CQG(95)gq; Embacher PRD(95)gq [action], CQG(96)gq/95, gq/95-conf; Kriele & Martin CQG(95) [singularities]; Martin PRD(95)gq [perturbations]; Alty & Fewster CQG(96)gq [initial value]; Dray JMP(96)gq [Einstein's equation]; Hellaby et al IJMPD(97)gq/99 [black holes]; Mohseni PLA(00) [6D]; Kamleh gq/00 [and generalized functions]; Mars et al PRL(01)gq/00, Gibbons & Ishibashi CQG(04)ht [and branes]; Nieto IJGMP(12)-a1107 [canonical gravity in 2 time + 2 space dimensions]; Magueijo et al PRD(14)-a1311 [in Cartan gravity].
@ And lqg / lqc: Mielczarek a1207-proc; Mielczarek et al IJMPD-a1411 [and silent initial conditions]; Bojowald & Mielczarek JCAP(15)-a1503 [implications]; Barrau & Grain a1607-CQG [consequences, black hole sector]; Bojowald & Brahma PRD(17)-a1610 [midisuperspace models and dilaton gravity], PRD(18)-a1610 [2D black-hole models]; Mielczarek & Trześniewski PRD(17)-a1612 [invariant energy scales, hypersurface deformation algebra, spectral dimension]; Bojowald & Brahma PRD(20)-a2011 [and the no-boundary proposal].
@ And quantum gravity: Martin PRD(94)gq; Carlini & Greensite PRD(95)gq [and sqrt action]; Darabi & Rastkar GRG(06)gq/04 [and cosmological constant]; White et al CQG(10); Ghaneh et al IJMPD(13) [and GUP]; > s.a. boundary conditions in quantum cosmology [Hartle-Hawking]; quantum geometrodynamics.

Complex Extensions of General Relativity
@ References: Woodhouse IJTP(77); Boyer et al in(80); Ko et al PRP(81); Esposito 95, gq/95-proc, in(93)gq/95; Esposito & Stornaiolo NCB(96)gq/95 [linear equations]; Batakis PLB(97)ht/96; Kao ht/00 [extra scalar]; Hess et al IJMPA(10), Caspar et al IJMPE(12)-a1202 [pseudo-complex extension]; > s.a. formulations of general relativity [other variables, including self-dual 2-forms].
@ Complex techniques: Boyer & Plebański JMP(77) [heavens]; Esposito gq/99 [long introduction]; Martina et al JPA(01)mp [solutions of heavenly equation]; Esposito IJGMP(05)ht/05 [intro]; Maran gq/05 [and reality constraints]; > s.a. BF theory; complex structures.
> Related topics: see singularities [extending the spacetime].

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