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.
@ References: Jantzen PLB(87)gq/03 [cosmological]; Rendall gq/95-in; Choquet-Bruhat et al PRD(00)gq/99 [asymptotically euclidean, existence]; > s.a. gravitating matter, types of metrics.

With Maxwell Fields > s.a. collapse; 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.
@ Einstein-Maxwell: Carter CMP(68); Esposito & Witten PRD(73); Moncrief CQG(90) [U(1) symmetry]; Hogan et al LMP(98) [colliding waves]; 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].
@ Einstein-Maxwell, spherical: Thiemann NPB(95)gq/99 [with cosmological constant, reduced phase space]; Sarbach & Lehner PRD(04)ht/03 [(no) naked singularities].
@ Einstein-Maxwell, static: Deser & Mazur CQG(85) [3D]; Chandrasekhar PRS(89); Ocariz & Rago GRG(94)gq; Komathiraj & Maharaj GRG(07) [spherical].
@ Einstein-Maxwell + dilaton: 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]; > s.a. Robinson-Bertotti [spherical]; Reissner-Nordström; types of spacetimes; wave solutions.

With Other Matter > s.a. collapse; cosmological models; gravitating matter; 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, > 0]; Ibadov et al PLB(05) [axisymmetric]; > s.a. Kundt Waves.
@ 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].
@ Scalar fields: Christodoulou CPAM(93) [bounded-variation solutions]; Saha & Shikin gq/01 [+ spinor, plane-symmetric]; Gaudin et al IJMPD(06) [static]; > s.a. Lichnerowicz Equation..
@ 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]; Bratek et al APPB(07)gq/06 [differentially rotating dust]; > s.a. Wahlquist.
@ Other extended matter: Gamboa Saraví GRG(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]; > s.a. Bonnor-Swaminarayan.
> Other fields: see dilaton; dirac fields in curved spacetime; klein-gordon fields.
> Other types of solutions: see axisymmetry; black-hole solutions; solutions with symmetries; solution-generating methods; spherical symmetry.

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

With Distributional Sources > s.a. gravitating matter [shells]; 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 -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 a0901.
@ Planar matter shells: Dray & 't Hooft CQG(86).

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send feedback and suggestions to bombelli at olemiss.edu – modified 7 aug 2009