Spherical Symmetry in General Relativity  

In General > s.a. computational physics [scalar fields]; spherical harmonics; spherically symmetric geometries \ types of spacetimes.
@ References: Deser et al CQG(04)gq [re shortcut in metric Ansatz]; Jacobson CQG(07)-a0707 [radial-area coordinate and line element]; Abreu & Visser PRD(10)-a1004 [geometrically preferred coordinate system]; Moopanar & Maharaj IJTP(10)-a1108 [conformal symmetry]; Cordero-Carrión et al JMP(11)-a1111 [maximal slicings]; Tupper et al CQG(12)-a1206 [complete classification in terms of local conformal symmetries]; Parry AMP(14)-a1210 [survey]; Kim et al a1604 [tetrad-based method].
@ Static: Ali et al TMP(15)-a1309 [complete classification using Noether symmetries]; Santa & Romano a1611 [cosmological interpretation].
@ Locally rotationally symmetric spacetimes: Sharif & Amir BJP(10)-a1002; Amir & Sattar IJTP(14)-a1312 [vacuum solution in f(R) gravity].
> Related topics: see Hypersurface [representations of deformation generators]; models in canonical gravity; perturbations; Trapped Surface.

In Vacuum General Relativity > s.a. Birkhoff's Theorem; gravitational 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, ch13; 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); Hájíček 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]; Molina et al PRD(11)-a1107 [isotropic extensions].
> Special solutions: see Penrose Inequality; black-hole solutions; schwarzschild spacetime; schwarzschild-de sitter space.

With Fluids > s.a. Lemaitre-Tolman-Bondi; types of singularities.
* Solutions: McVittie; Oppenheimer-Snyder; Friedmann-Lemaître-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]; Tewari & Joshi Pant a1006 [static perfect fluid].
@ With dust: Casadio PRD(98)gq [Hamiltonian]; Humphreys et al GRG(12)-gq/98 [classification]; Carr PRD(00)gq [self-similar]; Gladush OAP-a1011 [charged dust, stable].
@ 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 PRD(08)-a0707, Maeda et al PRD(08)-a0707 [dark energy].

With Other Matter > s.a. gravitational collapse; dirac fields; numerical general relativity; solutions with matter.
* With massless scalar, static: Janis-Newman-Winicour; Wyman; Fisher.
* Results: If R s = GM / c2, there are no solutions with matter support R < R s; for R = R s + ε, 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]; Abdolrahimi & Shoom PRD(10)-a0911 [massless, Fisher solution]; Bhattacharya & Joshi MPLA(11)-a0912 [massless]; Azreg-Aïnou GRG(10)-a0912 [self-interacting]; Bronnikov et al EPJC(11)-a1109 [stability]; Álvarez et al PRL(12)-a1111 [local Hamiltonian]; Gambini & Pullin CQG(13)-a1207 [with local Hamiltonian, complete initial-boundary value problem].
@ Einstein-scalar, with cosmological constant: Mehrpooya & Momeni IJMPA(10)-a0903; Costa et al AHP(13)-a1206 [characteristic initial data].
@ 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]; Künzle & Oliynyk JGP(06)-a0810 [Einstein-Yang-Mills-Higgs]; Slagter IJMPD(09)-a0803 [+ Gauss-Bonnet]; Bartnik et al a0907 [SO(5)]; Lübbe & Valiente Kroon PRD(14)-a1403 [anti-de Sitter-like].
@ 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; Hájíček PRD(98)gq/97, PRD(98)gq, & Bičák PRD(97)gq; Hájíček 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. Bertrand Spacetimes; higgs field; kantowski-sachs metrics; monopoles; Nariai Metric; perturbations; solitons; wormhole solutions.

In Modified Theories > s.a. canonical quantum gravity; quantum black holes; semiclassical gravity.
@ f(R) theories: Barraco & Hamity PRD(00) [first-order formalism]; Multamäki & Vilja PRD(06)ap; Clifton CQG(06)gq-MGXI, PhD(06)gq, comment Faraoni CQG(09)-a0909; Navarro & Van Acoleyen JCAP(07)gq/06 [acceleration and other phenomenology]; Multamaki & Vilja PRD(07)ap/06 [pfluid]; Barausse et al CQG(08)gq/07 [no static polytropic spheres]; Capozziello et al CQG(07)gq [Noether symmetry approach]; Kainulainen et al PRD(07)-a0704; Saffari & Rahvar MPLA(09)-a0710 [consistency issue]; Kainulainen & Sunhede PRD(08)-a0803 [stability]; Capozziello et al CQG(08); Nzioki et al PRD(10)-a0908; Pandey & Sinha a0911; Capozziello et al GRG(12)-a1204 [and Noether symmetries]; Gao & Shen GRG(16)-a1602 [static].
@ Other higher-order gravity: Dean PhD(00)-a1312 [and orbital analysis]; Seifert PRD(07)gq [instability, also Einstein-aether and TeVeS]; Deser et al GRG(08)-a0705 [Einstein + non-polynomial]; Mazharimousavi & Halilsoy PLB(10)-a1007 [Lovelock gravity + Yang-Mills fields]; Kunstatter et al CQG(12)-a1201 [Lovelock gravity]; Lü et al PRD(15)-a1508 [with quadratic curvature terms]; > s.a. modified electromagnetism [coupled to non-linear theory].
@ f(T) gravity: Wang PRD(11)-a1102 [+ Maxwell theory]; Böhmer et al CQG(11)-a1107 [stars]; Daouda et al EPJC(11)-a1108, Ferraro & Fiorini PRD(11)-a1109 [static]; Atazadeh & Mousavi EPJC(13)-a1212; Nashed GRG(13)-a1502; Paliathanasis et al PRD(14)-a1402 [Schwarzschild-like solutions].
@ 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 Λ]; Adler & Ramazanoğlu IJMPD(15)-a1308 [gravity with trace-dynamics modifications]; Li et al CQG(16)-a1503 [in Lorentz-breaking massive gravity]; > s.a. Conformal Gravity; gauge-theory solutions; massive gravity; theories of gravitation.

main pageabbreviationsjournalscommentsother sitesacknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 28 may 2017