Solutions
of Einstein's Equation with Matter| Solutions
of Einstein's Equation with Matter |
In General > s.a. [einstein's
equation; solutions]; 3D
gravity; black holes; higher
order gravity; kaluza-klein.
@ 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.
@ Particles: Aichelburg & Sexl GRG(71);
Rendall gq/02-ln
[Einstein-Vlasov];
Fiziev gq/03, gq/04 [massive
point particle?]; > 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.
dS.
@ Lambda < 0: Anderson et al JHEP(02) [vacuum, static]; Chrusciel &
Delay gq/05 [vacuum,
stationary]; > s.a. AdS.
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].
@ Planar matter shells: Dray & 't Hooft CQG(86).
Main page – Abbreviations – Journals – Comments – Other
sites – Acknowledgements
Send feedback and suggestions to bombelli at olemiss.edu – Modified
5 jul 2008