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];
Deser a1810 [matter covariantization];
Kovtun & Shukla a1907 [effective equations in matter];
Lin & Lalak a1911,
Bini & Esposito a2101 [novel types of matter coupling];
> 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),
Schneiter et al CQG(18)-a1804 [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];
Vancea a1911 [field lines];
> 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. charges; 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 CQG(16)-a1510 [status of the shear-free fluid conjecture];
> s.a. multipole moments; solution-generating
methods [gravity-fluid correspondence]; Wahlquist Metric.
@ Einstein-Vlasov system: Rendall gq/02-ln;
> s.a. minkowski space [stability]; solutions with symmetries.
@ Other extended matter: Gamboa Saraví GRG(09),
IJMPA(09),
Kamenshchik & Vardanyan PLB(19)-a1811 [static, plane-symmetric, constant-density slabs].
@ Particles:
Duan JETP(54)-a1705 [pointlike charge];
Aichelburg & Sexl GRG(71);
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; tachyons.
> 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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