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 JCAP(18)-a1611 [cosmological interpretation].
@ Locally rotationally symmetric spacetimes:
Sharif & Amir BJP(10)-a1002;
Amir & Sattar IJTP(14)-a1312 [vacuum solution in f(R) gravity];
MacCallum a2104 [criteria].
> 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];
Jackson a1808-PhD [numerical].
@ 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"];
Saha a2008 [types of matter];
> 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];
Rodrigues-da-Silva & Medeiros PRD(20)-a2004;
> 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];
Golovnev & Guzmán a2103 [approaches].
@ 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];
Murk & Terno a2012 [consistency constraints];
> s.a. Conformal Gravity; gauge-theory solutions;
Gauss-Bonnet Gravity; massive gravity;
theories of gravitation.
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