Wormhole Solutions  

In General > s.a. constraints for general relativity [gluing solutions]; electromagnetism in curved spacetime; kaluza-klein models.
* Metric: For a static, spherically symmetric wormhole connecting two asymptotically flat (or AdS) regions,

ds2 = –a2(l) dt2 + dl2 + r2(l) dΩ2 ,   or   ds2 = –exp{–2φ(r)}dt2 + [1–b(r)/r]–1dr2 + r22 ,

where φ(r) is the "redshift function" (e.g., φ(r) = 0) and b(r) the "shape function" (e.g., b(r) = rt2/r, r2(l) = r2t + l2).
* Tolman wormhole: A bounce replacing the initial singularity; > s.a. Tolman Solution.
@ Existence, uniqueness: Jungman & Wald PRD(89); Ruback CQG(89); Kuhfittig ASTP-a1001 [large families of solutions].
@ Einstein-Rosen bridge / Schwarzschild wormhole: Collas & Klein AJP(12)mar [embeddings]; Goyal & Gupta PS(12) [symmetries and exact solutions]; Katanaev MPLA(14) [test-particle motion].
@ Other specific solutions: Frolov et al PLB(89); González-Díaz PRD(89); Keay & Laflamme PRD(89); Laflamme pr(89); Moss pr(89); González-Díaz MPLA(90); Harris AJP(93)dec [connecting Reissner-Nordström spacetimes]; Teo PRD(98)gq; Bronnikov & Skvortsova G&C(14)-a1404-conf [cylindrically and axially symmetric]; Gibbons & Volkov a1606 [from duality rotations and complex transformations].
@ With cosmological constant: Lemos et al PRD(03)gq [and rev]; Maldacena & Maoz JHEP(04) [in anti-de Sitter];
@ Other cosmological: Kim PRD(96) [in FLRW spacetime, traversable, non-exotic matter]; Molina-Paris & Visser PLB(99)gq/98 [FLRW spacetime from bounce]; Mirza et al IJMPD(06)gq; Maeda et al PRD(09)-a0901 [dynamical]; Ebrahimi & Riazi PRD(10), ASS-a0905 [(n+1)-dimensional]; Bochicchio & Faraoni PRD(10)-a1007 [Lemaître-Tolman-Bondi wormhole].
@ Rotating solutions: Khatsymovsky PLB(98)gq; Kuhfittig PRD(03)gq/04; Kashargin & Sushkov G&C(08)-a0710, PRD(08) [scalar with negative kinetic energy]; Dzhunushaliev et al PRD(13)-a1309 [5D]; Kleihaus & Kunz PRD(14)-a1409 [in 4D]; Bronnikov a1509 [no-go result].
@ Analysis of solutions: Hochberg & Visser PRD(97)gq [traversable]; Visser & Hochberg gq/97-proc; Matos et al a1203 [Kerr-like wormhole supported by phantom matter, ring singularity and censorship]; Olmo et al CQG(16) + CQG+ [curvature divergences and physical observers].
@ Stability: Vollick PRD(97)gq/98, Bronnikov & Grinyok G&C(01)gq/02 [+ scalar field]; Shinkai & Hayward PRD(02)gq [numerical]; Correa & Troncoso JHEP(08)-a0805 [asymptotically AdS, with scalar]; González et al CQG(09)-a0806, CQG(09)-a0806 [with ghost scalar field]; Novikov et al ARP(09)-a0911; Bronnikov et al G&C(13)-a1312 [stable solution]; Kuhfittig FJMP-a1409 [thin-shell wormholes are unstable].
@ Lorentzian: Morris & Thorne AJP(88)may; Morris et al PRL(88); Visser NPB(89)-a0809, PRD(89)-a0809, PLB(90), PRD(90); Abbott & Farhi NPB(90); Hochberg & Kephart PLB(91), PRL(93); Kar & Sahdev PRD(96); Rosales IJMPA(98) [vacuum decay]; Dadhich et al PRD(02)gq/01 [R = 0]; Müller AJP(04)aug [visual appearance]; Nandi et al NPCS(06)gq/04 [viability]; Nandi & Zhang PRD(04), et al PRD(04) [stringy]; Kuhfittig a0908-talk [and quantum field theory constraints]; Culetu PS(15)-a1407 [properties of a Misner-Thorne wormhole]; Rahaman et al PLB(15)-a1505 [inspired by non-commutative geometry].
@ Lorentzian, n-dimensional: Cataldo et al PRD(02) [self-dual]; Cataldo et al PRD(11) [with a cosmological constant]; Kar et al a1505 [in scalar-tensor theory with extra dimensions]; Estevez et al a1611 [in braneworld].
@ Non-existence results: Saa MPLA(99)gq; Arellano & Lobo CQG(06) [with non-linear electromagnetism]; Kuhfittig FJMP-a0904 [with spacetime-dependent cosmological constant].
@ 2+1: Carlip pr(90); Åminneborg et al CQG(98)gq/97, CQG(99)gq/98; Brill gq/99-proc; Larrañaga a0706, JGPO(07)-a0707 [agujeros de gusano]; Skenderis & van Rees CMP(11) [holographic interpretation].
@ Other types: Twamley & Page NPB(92) [imaginary]; Diemer & Hadley CQG(99)gq [with topological charge]; Maeda PRD(09)-a0811 [formation model]; Kuhfittig CEJP(11)-a1104 [charged]; Kuhfittig AJMP-a1311 [Hayward wormholes].

@ General references: Ford & Roman PRD(96) [and quantum field theory]; Khatsymovsky PLB(97)gq/96; Konstantinov gq/97 [mixed boundary problem]; Ida & Hayward PLA(99)gq [negative energy]; Hayward PRD(02)gq [ghost radiation]; Kuhfittig PRD(02)gq/04, PRD(03)gq/04, gq/05, Fewster & Roman PRD(05)gq [and exotic matter]; Zaslavskii PRD(07)-a0707 [minimal violation of nec]; Lobo IJMPD(16) [in general relativity and modified theories].
@ Traversable solutions: Anchordoqui et al MPLA(00)gq/99 [scalar-tensor]; Krasnikov PRD(00)gq/99 [massless ν, γ, or φ]; Hayward gq/02-conf; Armendáriz-Picón PRD(02)gq; Bronnikov & Grinyok G&C(01)gq/02 [+ scalar field], gq/02-fs [+ electromagnetism + scalar field]; Hellaby & Krasiński PRD(02)gq [Szekeres wormhole]; Visser et al PRL(03) [small E violations]; Lobo CQG(04)gq [shells]; Koyama & Hayward PRD(04)gq, Hayward & Koyama PRD(04) [from Schwarzschild]; Kim et al PRD(04) [in 2+1]; Lobo PRD(06) [with Chaplygin gas]; Böhmer et al PRD(07)-a0708 [conformally symmetric]; Kuhfittig a0802-conf [with Chaplygin gas], CEJP(10)-a0903; Shatskiy et al PU(08)-a0810 [exact solution]; Montelongo & Zannias CQG(09) [initial-value approach]; Lobo & Mimoso PRD(10)-a0907; Balakin et al PRD(10)-a1003 [in non-minimal Einstein-Maxwell theory]; Montelongo et al PRD(12)-a1112 [thin-shell]; Garattini a1311-proc [from Gravity's Rainbow]; Butcher PRD(15)-a1503; Duplessis & Easson PRD(15)-a1506 [in quadratic gravity]; Clément et al PRD(16)-a1509 [supercritically charged black holes with NUT charge].
@ Traversable, with phantom matter: Lobo PRD(05)gq, PRD(05); Kuhfittig CQG(06)gq, GRG(09)-a0904.

In Modified Gravity / With Other Types of Fields > s.a. Galileon Field; Lovelock Gravity; wormholes [and quantum gravity].
@ Brans-Dicke theory: Coule MPLA(98), Agnese & La Camera ht/01-MG9; Lu et al NCB(03); Bhadra & Sarkar MPLA(05); Bhattacharya et al CQG(09)-a0910; Lobo & Oliveira PRD(10)-a1001; Eiroa & Simeone PRD(10); Bhattacharya et al CQG(11)-a1107; Tretyakova et al CQG(15)-a1504.
@ Scalar-tensor gravity: Shaikh & Kar a1604 [satisfying the weak energy condition].
@ In f(R) theories: Furey & DeBenedictis CQG(05)gq/04 [Rn gravity]; Lobo & Oliveira PRD(09)-a0909; Oliveira MS-a1107; Saiedi & Esfahani MPLA(11)-a1409 [time-dependent]; DeBenedictis & Horvat GRG(12)-a1111; Dent et al a1608 [in R2 gravity, stability].
@ Other higher-order theories: Richarte & Simeone PRD(07)-a0710 [with ordinary matter]; Bronnikov et al G&C(10)-a1005 [and scalar-tensor gravity]; Kuhfittig ASTP(13)-a1311 [f(R) theories and the weak energy condition].
@ Theories with torsion: Anchordoqui MPLA(98)gq/96; Azizi IJTP(13)-a1205 [in f(R,T) gravity].
@ With phantom energy: Zaslavskii PRD(05); Rahaman et al PLB(06), PS(07)-a0705; González et al PRD(09)-a0906.
@ Hořava gravity: Botta Cantcheff et al PRD(10); Bellorín et al PRD(14)-a1404.
@ Other theories: Kim gq/97 [Euclidean Taub model], NPB(98)ht/97 [axionic], NPB(98)ht/97 [in Einstein-Yang-Mills]; Vollick CQG(99) [string theory]; Faraoni & Israel PRD(05)gq/05 [FLRW spacetime and big rip]; Nashed APPA(07)gq/05 [teleparallel]; Chiodaroli & Gutperle PRD(09)-a0901 [N = 2 supergravity]; Dehghani & Hendi GRG(09)-a0903 [Gauss-Bonnet-Born-Infeld]; Richarte & Simeone PRD(09) [Einstein-Born-Infeld]; Kanti et al PRL(11)-a1108 [4D dilatonic Einstein-Gauss-Bonnet theory]; Harko et al PRD(13)-a1301 [modified gravity without exotic matter]; Rahaman et al EPJC(16)-a1607 [Finsler geometry].

Similar Spacetimes > s.a. causality violations [warp drive].
@ Krasnikov tube: Krasnikov PRD(98)gq/95; Everett & Roman PRD(97)gq.
@ Analogs: Nandi et al gq/04 [acoustic].

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