Solutions of Einstein's Equation with Matter  

In General > s.a. einstein's equation; solutions / 3D gravity; black holes; higher-order gravity; kaluza-klein theory.
* Geometrization of a matter field: Conditions on a spacetime metric for it to be part of a solution of the Einstein equation with the given type of matter.
@ References: Jantzen PLB(87)gq/03 [cosmological]; Rendall gq/95-GR14; Choquet-Bruhat et al PRD(00)gq/99 [asymptotically euclidean, existence]; Kiosak & Matveev JGP(14)-a1302 [there exist no 4D geodesically equivalent metrics with the same stress-energy tensor]; Krongos & Torre a1503 [geometrization conditions for perfect fluids, scalar fields, and electromagnetic fields]; > s.a. gravitating matter; types of metrics.

With Maxwell Fields > s.a. gravitational collapse; multipole moments; phenomenology.
* Results: A general 5-parameter family of solutions of the electrovac Einstein equation (= Einstein-Maxwell), including all stationary black holes, Taub-NUT and (anti)de Sitter was found by Carter in 1968; > s.a. Papapetrou-Majumdar Metrics.
@ General references: Carter CMP(68); Esposito & Witten PRD(73); Moncrief CQG(90) [U(1) symmetry]; Finster et al PLA(99)gq/98 [+ Dirac, particlelike solutions]; Ivanov JMP(99)gq/01 [algebraically special]; Socorro & Cornejo gq/01 [axisymmetric]; Ida & Uchida PRD(03)gq [D-dimensional stationary]; Fischer gq/05 [similarity, 1 Killing vector]; Bonnor GRG(06) [properties]; Ernst et al JPCS(10)-a1006 [on Sibgatullin's and Alekseev's approaches]; Hruška & Žofka CQG(11) [non-trivially conformally related solutions]; Torre CQG(14)-a1308 [local geometric conditions for a null electrovacuum spacetime]; Lysov a1310 [from solutions of the equations of magnetohydrodynamics]; Smolić et al CQG(16)-a1508 [3D, in spacetimes with symmetries].
@ Waves: Ji et al IJTP(98) [intense laser beam]; > s.a. gravitational wave solutions [colliding waves].
@ Spherical solutions: Thiemann NPB(95)gq/99 [with cosmological constant, reduced phase space]; Liu & Zhang JMP(02)gq [star and background radiation]; Petri gq/03; Sarbach & Lehner PRD(04)ht/03 [(no) naked singularities]; Díaz-Alonso & Rubiera-García PRD(10)-a0908 [non-linear electrodynamics]; Burke & Hobill a0910 [physically realistic charged fluid]; Costa et al CQG(15)-a1406 [with scalar and cosmological constant, well-posedness]; > s.a. reissner-nordström solutions.
@ Static solutions: Deser & Mazur CQG(85) [3D]; Chandrasekhar PRS(89); Ocariz & Rago GRG(94)gq; Komathiraj & Maharaj GRG(07) [spherical].
@ With dilaton fields: Gibbons NPB(82), & Maeda NPB(88) [black holes]; Garfinkle et al PRD(91); Zloshchastiev PRD(01)ht; Dunajski CQG(06)gq; > s.a. black-hole solutions.
@ Special types: Lu GRG(05) [with magnetic dipoles]; Posada & Batic CEJP(14)-a1310 [with a cosmological constant]; Füzfa PRD(16)-a1504 + news IBT(16)jan [spacetimes around current loops and solenoids]; > s.a. Robinson-Bertotti [spherical]; Melvin Solution; types of spacetimes.

With Other Matter > s.a. collapse; cosmological models; gravitating bodies; Lemaître-Tolman-Bondi; Vaidya.
@ Einstein-Yang-Mills: Bartnik & McKinnon PRL(88) [asymptotically flat]; Smoller & Wasserman JMP(95); Rudolph et al JMP(99) [+ Dirac]; Breitenlohner et al CMP(06)gq/04 [static, spherical, Λ > 0]; Ibadov et al PLB(05) [axisymmetric]; > s.a. Kundt Waves.
@ Einstein-Yang-Mills, cosmological: Gal'tsov & Volkov PLB(91); Darian & Künzle JMP(97); Rudolph et al JMP(99) [+ Dirac]; Breitenlohner et al PLB(00)gq [+ Higgs, static; Emoto et al PTP(02)ht [Einstein-electroweak]; Füzfa CQG(03)gq [instability]; Gal'tsov a0901-conf [non-abelian condensates and dark energy]; Elizalde et al PAN(13)-a1201.
@ Einstein-Yang-Mills + dilaton: Brihaye & Radu PLB(06)gq [euclidean]; > s.a. Kantowski-Sachs models.
@ Einstein-Yang-Mills + Higgs: van der Bij & Radu NPB(00)ht; Forgács & Reuillon PRL(05) [static, spherical, spatially compact]; > s.a. initial-value problem.
@ Einstein-scalar: Christodoulou CPAM(93) [bounded-variation solutions]; Saha & Shikin gq/01 [+ spinor, plane-symmetric]; Gaudin et al IJMPD(06) [static]; Pugliese & Valiente GRG(13)-a1301 [charged scalar field, evolution equations]; Reiris a1507 [static]; > s.a. Lichnerowicz Equation.
@ Einstein-scalar, cosmological: Williams et al gq/04-in [isotropic and anisotropic]; Cannata et al PLB(09) [with singularity at finite scale factor].
@ Quintessence / dark energy: Gu & Hwang PLB(01)ap, PRD(06)ap/01; Wetterich SSR(02)ap/01; González-Díaz PRD(02)ht; Alam et al MNRAS(03)ap; Gruppuso & Finelli PRD(06)ht [dust + dark energy]; > s.a. cosmological constant.
@ Monopoles: Manko & Ruiz CQG(98) [multi-solitons]; Maison & Liebling PRL(99); Lue & Weinberg PRD(00)ht, GRG(00)gq.
@ Fluids: Coley PLA(89) [non-perfect]; Ferrari & Ibáñez CQG(89) [effective fluid from null-field interaction]; Bonnor CQG(94) [emitting null fluid]; Sussman CQG(98)gq/97, & Triginer CQG(99)gq/98 [ideal gas]; Perjés AdP(00)gq/99-conf [with perfect fluids, inhomogeneous]; Bratek et al APPB(07)gq/06 [differentially rotating dust]; Fang & Gao PRD(14)-a1311 [general proof of the entropy principle]; Van den Bergh & Slobodeanu a1510 [status of the shear-free fluid conjecture]; > s.a. multipole moments; solution-generating methods [gravity-fluid correspondence]; Wahlquist Metric.
@ Other extended matter: Gamboa Saraví GRG(09), IJMPA(09) [static, plane-symmetric slabs].
@ Particles: Aichelburg & Sexl GRG(71); Rendall gq/02-ln [Einstein-Vlasov]; Fiziev gq/03, gq/04 [massive point particle?]; Meissner a0901 [point mass in de Sitter spacetime]; Katanaev GRG(13)-a1207 [massive point particle?]; Bruneton a1303-MG13 [cubic lattice of spherical masses]; > s.a. Bonnor-Swaminarayan Solutions.
> Other fields: see dilaton; dirac fields in curved spacetime; Chameleon Fields; klein-gordon fields; Phantom Fields.
> Other types of solutions: see axisymmetry; black holes; solutions with symmetries; solution-generating methods; spherical symmetry.

With Distributional Sources > s.a. gravitating matter [shells, weak solutions]; metric matching; solutions [defects]; types of metrics.
* Result: There is no solution corresponding to a matter stress-energy with support on a timelike line; This means that particles cannot be thought of as δ-function distributions of matter (maybe as black holes?).
@ General references: Geroch & Traschen PRD(87) [strings]; Pantoja & Rago IJMPD(02)gq/00; Steinbauer & Vickers CQG(06)gq [and other generalized functions]; Gemelli IJTP(07)-a0704 [regular discontinuities]; Gravanis & Willison JMP(09)-a0901.
@ Planar matter shells: Dray & 't Hooft CQG(86).

Cosmological Solutions > s.a. bianchi models; cosmological models; generalized cosmological models; solutions with symmetries.
@ Λ > 0: Andersson & Galloway ATMP(0)ht [topology]; Rendall AHP(04)gq/03 [asymptotics]; Chapline & Marecki a0709 [rotating].
@ Λ < 0: Anderson et al JHEP(02) [vacuum, static]; Chruściel & Delay AHP(07)gq/05 [vacuum, stationary].
> Specific types of solutions: see anti-de sitter space; de sitter space; Robinson-Trautman Solutions; schwarzschild-de sitter spacetime.


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