Spherical Symmetry in General Relativity  

In General > s.a. computational physics [scalar field theory]; models in canonical gravity; perturbations; spherical harmonics.
$ Pseudospherically symmetric spacetime: A spacetime, invariant under the action of the 3D Lorentz group, whose surfaces of transitivity are timelike and 2D, with line element ds2 = –s2 [(1–x2)–1 dx2 – (1–x2) dt2].
@ References: Deser et al CQG(04)gq [re shortcut in metric Ansatz]; Jacobson a0707-CQG [radial-area coordinate and line element].

In Vacuum General Relativity > s.a. Birkhoff's Theorem; collapse; foliations; thermodynamics; vacuum [polarization].
* Vacuum solution: There is only one, and it is static, the Schwarzschild solution (> see Birkhoff's Theorem); This is because of the spin-2 nature of the gravitational field; its source is a quadrupole changing in time.
* Perturbations: Tensors such as metric perturbations can be decomposed using tensor spherical harmonics.
@ General references: in Bergmann 42, ch 13; in Synge 60; Bergmann et al JMP(65); Takeno 66; Thomi et al PRD(84); Clarke CQG(87); in Harriott & Williams IJTP(89); Siegl CQG(92); Kastrup & Thiemann NPB(94)gq [as integrable system]; Braham PRD(95); Dadhich CS(00)gq [duality].
@ Hamiltonian: Berger et al PRD(72); Lund PRD(73) [Schwarzschild]; Unruh PRD(76); Hájícek PRD(84), PRD(84), PRD(84), PRD(85), PRD(85); Guven & Ó Murchadha PRD(95)gq/94, PRD(95)gq/94; Hayward PRD(96)gq/94 [energy]; Lau CQG(96)gq/95.
@ Related topics: Malec PRD(94) [horizons]; Guven & Ó Murchadha PRD(97)gq, PRD(97)gq [apparent horizons]; Abbassi JHEP(99) [+ cosmological constant]; Nashed PRD(02)gq [non-singular black holes, teleparallel theory].
> Special solutions and related topics: see Penrose Inequality; black hole solutions; schwarzschild; schwarzschild-de sitter.

With Fluids > s.a. Lemaitre-Tolman-Bondi; types of singularities.
* Solutions: McVittie; Oppenheimer-Snyder; Robertson-Walker.
@ General references: Berger et al JMP(87) [static pfluids]; Beig & Simon LMP(91) [uniqueness result]; Sharif & Iqbal ChJP(02)gq/04 [non-static]; Salgado PRD(02)gq [fluid + particles]; Lake PRD(03)gq/02 [static, all]; Giambò et al CMP(03)gq/02 [anisotropic elastic materials]; Feroze et al NCB(03) [non-static]; Heinzle CQG(03) [static]; Das et al JMP(03)gq, Negi IJTP(06)gq/04 [interiors]; Wiltshire CQG(06)gq; Herrera et al PRD(08)-a0712 [static, anisotropic].
@ With dust: Casadio PRD(98)gq [Hamiltonian]; Humphreys et al gq/98 [classification]; Carr PRD(00)gq [self-similar].
@ Einstein-Vlasov: Andréasson & Rein CQG(07) [steady states].
@ Self-similar: Carr et al PRD(00)gq/99, CQG(01)gq/99; Carr & Coley PRD(00)gq/99, CQG(00)gq; Wagh & Govinder GRG(06)gq/01, gq/01; Carr & Gundlach PRD(03)gq/02; Sharif & Aziz IJMPD(05); Harada et al a0707, Maeda et al a0707 [dark energy].

With Other Matter > s.a. collapse; dirac fields; numerical general relativity; soliton; solutions with matter; wormhole.
* With massless scalar, static: Janis-Newman-Winicour; Wyman.
* Results: If R s = GM / c2, there are no solutions with matter support R < R s; for R = R s + , the solution will be unstable; In the case of a perfect fluid, there are stable spherically symmetric solutions only for R > (9/8) R s.
@ Einstein-scalar: Christodoulou CMP(96), CMP(86) [massless, initial-value]; Kokubun MPLA(96); Malec JMP(97); Virbhadra IJMPA(97)gq [m = 0]; Bronnikov PRD(01)gq [causal structure]; Bilge & Daghan gq/05/GRG [partial decoupling].
@ Einstein-Maxwell: Liu & Zhang JMP(02)gq [star and background radiation]; Petri gq/03.
@ Einstein-Yang-Mills: Oliynyk & Künzle JMP(02)gq/00 [boundary value problem], CQG(02)gq [global behavior], CQG(03); Linden CMP(01), JMP(01) [non-compact, static, SU(2)]; Oliynyk gq/02-wd [Einstein-Yang-Mills-dilaton]; Brihaye & Hartmann CQG(05)ht/04 [4 + d dimensions, + cosmological constant]; Slagter a0803 [+ Gauss-Bonnet].
@ With matter shells: Dray CQG(90) [joining Reissner-Nordström spacetimes and collapsing shells]; Friedman et al PRD(97)gq; Zloshchastiev PRD(98)gq/97 [charged dust], gq/97; Hájícek gq/97, PRD(98)gq, & Bicák PRD(97)gq; Hájícek NPB(01)ht/00 [dynamics], & Kiefer NPB(01)ht/00 [embedding variables]; Mazur & Mottola gq/01 [gravastar].
@ Related topics: Petri gq/04 [string-like "holographic solution"]; > s.a. kantowski-sachs metrics; monopoles; Nariai Metric.

In Modified Theories > s.a. canonical quantum gravity; quantum black holes; semiclassical general relativity.
@ In higher-order gravity: Barraco & Hamity PRD(00); Multamäki & Vilja PRD(06)ap [f(R) theories]; Clifton gq/06-in, gq/06-PhD; Navarro & Van Acoleyen JCAP(07)gq/06 [acceleration and other phenomenology]; Multamaki & Vilja PRD(07)ap/06 [pfluid in f(R) gavity]; Seifert PRD(07)gq [instability, also Einstein-aether and TeVeS]; Capozziello et al CQG(07)gq [Noether symmetry approach]; Kainulainen et al PRD(07)-a0704; Deser et al a0705 [Einstein + non-polynomial]; Saffari & Rahvar a0710 [consistency issue]; Barausse et al a0803 [no static polytropic spheres]; Capozziello et al CQG(08); Kainulainen & Sunhede a0803 [stability].
@ Other theories: Minkevich & Vasilevski gq/03 [metric-affine gauge theory]; Wohlfarth CQG(04) [BF-like], comment Deser et al CQG(04)gq [re shortcut]; Bhadra & Sarkar GRG(05)gq [vacuum Brans-Dicke]; Esposito et al CQG(07) [variable G and cosmological constant]; > s.a. gauge theory solutions, gravitation.

Main page – Abbreviations – Journals – Comments – Other sites – Acknowledgements
Send feedback and suggestions to bombelli at olemiss.edu – Modified 24 jun 2008