Models for Spacetime Topology Change  

Dynamics: Generalized Einstein Equation > s.a. models in canonical general relativity [degenerate]; self-dual solutions of general relativity.
* Idea: Write down equations on a spacelike hypersurface which reduce to the Einstein equation when the variables give rise to allowed data for the Einstein equation, but which otherwise could describe more general situations than regular, non-degenerate metrics.
* Example: There is a hope, not yet realized, that the Ashtekar variables or related ones, could work.
@ Dynamics of spacetime topology: Spaans NPB(97)gq/96.

Dynamics: Quantum Topology Change > s.a. spacetime foam; topology change [phenomenology].
* In quantum cosmology: Probabilities of nucleation can be calculated for various topologies and dimensions; Then one can compare probabilities of different outcomes with the same Λ or the same E.
@ From quantum cosmology: Embacher CQG(96)gq/95, gq/95-conf; Shvedov PLB(96)gq, Rubakov & Shvedov PLB(96)gq, gq/96-proc [wormholes]; De Lorenci et al PRD(97)gq [canonical, FLRW]; Costa PRD(00)gq.
@ From quantum mechanics: Balachandran et al NPB(95)gq, IJMPA(00)ht/99 [2+1-dimensional geons]; Hadley IJTP(99)gq; Shapere et al a1210 [changes in unitarity-preserving boundary conditions]; Pérez-Pardo et al IJGMP(15)-a1501 [boundary dynamics and topology change]; > s.a. topology in physics.
@ Quantization of topology: Isham CQG(89); Isham, Kubyshin & Renteln CQG(90).
@ Related topics: Peleg MPLA(93) [from third quantization]; Ding et al PLB(95)gq/94, JMP(96)gq/95 [quantum tunneling]; Yu & Ford PRD(99)gq [fluctuations]; Martin et al JHEP(05)gq/00, Pinto-Neto et al IJMPA(05) [Green function, FLRW models]; Hartnoll CQG(03)ht [and compactification]; Dou & Ydri NPB(07) [quantum instability of gauge theory on fuzzy space]; Berenstein & Miller a1702 [from superpositions of classical states].

Specific Spacetimes
@ Trouser world: Kundt CMP(67); DeWitt in(84), in(85); Anderson & DeWitt FP(86); Anderson PLB(88), PRD(88); Manogue et al Pra(88); Daughton et al in-GR12; Harris & Dray CQG(90); Gratus & Tucker JMP(95)gq [particle production]; Braunstein gq/96; Krasnikov PRD(16)-a1601 [scalar field, flashless quantization]; Buck et al CQG(17)-a1609 [quantum scalar field in the Sorkin-Johnston state].
@ Pair creation: Sorkin IJTP(86); Dowker & García CQG(98)gq/97; Dowker & Surya PRD(98)gq/97.
@ Other: Borde PRD(97)gq/96 [regular black holes]; Bousso PRD(98)ht [proliferation of de Sitter space]; Friedman CQG(98) [no past boundary]; Ishihara et al CQG(06) [coalescing black holes in 5D]; Csizmadia & Rácz CQG(10)-a0911, Rahman a1506-MG14 [spherically symmetric collapse]; Kuhfittig AMP-a1207 [neutron-star interiors].

Topological Censorship
* Idea: Every causal curve in the domain of outer communications of scri having endpoints on scri can be deformed to scri; Therefore, an observer following one of those causal curves will not go through and probe a region of topology change.
* Results: Holds for a simply connected null scri, and under reasonable conditions for timelike scri.
@ General references: Friedman et al PRL(93)gq; Schleich & Witt in(94)gq/99; Browdy & Galloway JMP(95) [and black holes]; Burnett PRD(95)gq; Jacobson & Venkataramani CQG(95)gq/94; Galloway CQG(96), & Woolgar CQG(97)gq/96; Friedman & Higuchi AdP(06), a0801 [rev]; Krasnikov G&C(13)-a1007 [comments on the proof]; Eichmair et al JDG(14) [initial-data point of view]; > s.a. spacetime subsets [doc].
@ In asymptotically AdS spacetime: Galloway et al PRD(99)gq [black holes], PLB(01)ht/99 [AdS-cft].
@ Other extensions: Chruściel et al AHP(09)-a0808 [Kaluza-Klein spacetimes].

Types of Theories and Models > s.a. spacetime foam; topology change [degenerate]; wormholes [scale-dependent topology].
@ 2D: Ambjørn et al a0802-proc [causal dynamical triangulations].
@ 3D general relativity: Witten NPB(89); Fujiwara et al PRD(91), CQG(92) [quantum, with particles as defects]; Low CQG(92); Carlip & Cosgrove JMP(94)gq; Ionicioiu gq/97; Nesterov GRG(97)gq/04 [with non-abelian Higgs field].
@ Lattice quantum gravity: Carfora & Marzuoli CQG(92).
@ Regge calculus: Birmingham GRG(96).
@ Higher dimensions: Brill FP(86), Ionicioiu gq/97 [Kaluza-Klein]; Mazur NPB(87) [instability of toroidally compactified higher-dimensional Minkowski space]; Kol JHEP(05)ht/02; Gibbons & Ishibashi CQG(04)ht [brane world]; Butcher & Saffin JHEP(07) [compactified spacetimes]; Tanaka & Nagami IJGMP(11) [gauge group, G-cobordisms].
@ Strings / M-theory: Aspinwall et al PLB(93)ht, NPB(94)ht/93, in(95)ht/93, JMP(94); Greene et al JMP(01)ht/00; Aspinwall JHEP(04) [D-brane decay and Zariski topology]; Adams et al JHEP(05)ht [winding tachyons]; Kawai IJMPA(13).
@ Axion-induced: Giddings & Strominger NPB(88), NPB(88) [and quantum coherence].
@ And free quantum field theory: Marolf PLB(97)gq/96; Kim CQG(99)ht.
@ Non-commutative, fuzzy physics: Balachandran & Kürkçüoglu IJMPA(04)ht/03; Gratus JGP(04) [non-commutative algebras, sphere-torus]; de Albuquerque et al JHEP(04)ht [boundary conditions for Dirac operator]; Lee et al PRD(13)-a1212 [emergent gravity, without spacetime singularities].
@ Other models: Whiston IJTP(73), IJTP(74), IJTP(74), IJTP(75) [cobordism between whole spacetimes]; Finkelstein & Rodriguez IJTP(84); Kandrup & Mazur MPLA(90); Peleg MPLA(91) [change of dimension]; Magnon JMP(91); Alty JMP(95) [building blocks]; Krasnikov GRG(95) [check!]; Ionicioiu CQG(98) [Turaev-Viro theory]; Kirillov in(05)ap/04 [modified field theory and cosmology]; DeBenedictis et al PRD(08)-a0808 [phantom stars]; Frolov & Gorbonos PRD(09)-a0808 [curvature corrections]; Dzhunushaliev et al a0912 [as Ricci flow]; Lee et al PRD(13)-a1212 [emergent gravity from U(1) gauge fields on non-commutative spacetime]; Marunović & Prokopec PLB(16)-a1411 [phase transition and global monopole creation].

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