Schwarzschild-de Sitter Spacetime| Schwarzschild-de Sitter Spacetime |
In General > s.a. solutions of
einstein's equation / McVittie Metric.
* Idea: The natural generalization of
the Schwarzschild metric to the case of non-zero cosmological constant Λ.
* Line element: It can be written in
static form by replacing 1 − (2 GM/r) \(\mapsto\) 1 −
(2 GM/r) − (Λ r2/3)
in the Schwarzschild line element (> see schwarzschild
geometry), and one obtains the Kottler metric; It can also be obtained from the McVittie
metric, setting the expansion rate to be constant.
* Extreme case: The parameters satisfy
9Λ(GM)2 = 1 (in 4 spacetime dimensions).
Thermodynamics > s.a. black-hole
thermodynamics; black-hole radiation.
* Temperature:
In d dimensions, the temperature is given by
T = (d−3) (rH ± γ2rH) / 4π ,
where the upper (lower) sign holds in the Anti-de Sitter (de Sitter) case.
@ General references:
Brown et al PRD(94);
Teitelboim ht/02-proc [and stability];
Bolen & Cavaglià GRG(05)gq/04 [and gup];
Urano et al CQG(09)-a0903 [first law].
@ Entropy: Li NCB(01);
Ghezelbash & Mann JHEP(02)ht/01;
Shankaranarayanan PRD(03)gq;
Corichi & Gomberoff PRD(04)ht/03 [bounds];
Bolen & Cavaglià GRG(05)gq/04 [and gup];
Sekiwa PRD(06) [thermal cosmological constant].
@ Radiation:
Gibbons & Hawking PRD(77);
Bousso & Hawking PRD(98);
Hemming & Keski-Vakkuri PRD(01)gq/00;
Jiang CQG(07)-a0705;
Arraut et al CQG(09)-a0810 [two approaches];
Drouot a1510 [for massive bosons];
Pappas & Kanti PLB(17)-a1707;
Robson et al a1902 [temperature, topological approach].
@ Quantum: Nojiri & Odintsov PRD(99);
Nojiri & Odintsov IJMPA(00)ht/99.
Perturbations > s.a. perturbations of schwarzschild spacetime.
@ General references: Yoshino et al PRD(04)gq [Λ < 0].
@ Quasinormal modes, Schwarzschild-de Sitter:
Cardoso & Lemos PRD(03)gq [near-extremal];
Suneeta PRD(03)gq;
Maassen van den Brink PRD(03)gq;
Zhidenko CQG(04)gq/03;
Castello-Branco & Abdalla gq/03; Roy
Choudhuri & Padmanabhan PRD(04)gq/03,
comment Batic et al PRD(11)-a1105 [level spacing];
Konoplya & Zhidenko JHEP(04) [high overtones];
Medved & Martin GRG(05) [treatments].
@ Quasinormal modes, Schwarzschild-AdS:
Horowitz & Hubeny PRD(00);
Cardoso & Lemos PRD(01)gq [electromagnetism and gravity];
Konoplya PRD(02) [small black hole];
Moss & Norman CQG(02)gq [dS/AdS];
Musiri & Siopsis CQG(03)ht,
PLB(03),
PLB(03)ht;
Cardoso et al PRD(03)gq,
JMP(04);
Jing gq/05,
& Pan PRD(05) [Dirac fields];
Musiri et al PRD(06);
Daghigh JHEP(09)-a0901.
Similar Metrics > s.a. lovelock gravity.
* Nariai solutions: Degenerate
or extreme versions of the Schwarzschild-de Sitter metric; They are conformally non-flat,
singularity-free perfect fluid expanding cosmological models, satisfying the weak energy condition.
@ Nariai solutions: Dadhich gq/01;
Ortaggio PRD(02)gq/01 [impulsive waves];
Beyer CQG(09)-a0902 [generalized, positive cosmological constant];
Beyer a1012-MG12
[perturbations and the cosmic no-hair conjecture];
Fernando MPLA(13)-a1408,
IJMPD(14) [with quintessence].
@ With negative mass: Belletête & Paranjape IJMPD(13)-a1304-GRF.
@ Other modified metrics:
Wang et al CQG(09) [quantum deformed];
Fennen & Giulini CQG(15)-a1408 [static two-mass solution using Nariai spacetime].
References
> s.a. tests of general relativity with light.
@ General: Kottler AdP(18);
Socolovsky a1711 [rev];
Bugden & Paganini a1810 [the \(\Lambda\to0\) limit].
@ Geometry, coordinates:
Kamimura et al MPLA(91) [connection formulation];
Lake CQG(06)gq/05 [maximal extension];
Siddiqui GRG(11)-a1009 [foliation by flat spacelike hypersurfaces];
Brendle IHES-a1105
[hypersurfaces of constant mean curvature];
Fernandes et al a1910 [extremal surfaces];
Manjunatha et al IJGMP(20)-a2006 [curvature invariants].
@ Test particles, geodesics:
Stuchlík & Hledík PRD(99);
Kraniotis & Whitehouse CQG(03) [and precession];
Béssa & Lima IJMPD(04)gq [turning points];
Carvalho et al MPLA(04),
Cruz et al CQG(05)gq/04 [Schwarzschild-AdS];
Sultana & Dyer GRG(05);
Hackmann & Lämmerzahl PRL(08)-a1505,
PRD(08)-a1505 [complete analytic solution];
Dymnikova et al G&C(08) [overview];
Klein & Collas PRD(10) [recessional velocities and Hubble's law];
Arakida IJTP(13)-a1212,
comment Ovcherenko & Silagadze UJP(16)-a1511 [and periastron precession];
> s.a. spinning particles;
tests of general relativity with orbits.
@ Other classical matter:
Islam PLA(83) [planet and light motion];
Bijalwan a1108 [interior].
@ Fields, scalar: Brady et al PRD(99)gq [falloff];
Brevik & Simonsen GRG(01) [numerical].
@ Fields, other: Brady et al PRD(97) [tails];
Molina et al PRD(04)gq/03 [scalar, electromagnetic, and gravitation];
Lyu & Gui IJTP(04),
NCB(04),
PS(07) [Dirac fields];
Mackay et al EPL(05)ap [vp < 0 electromagnetic waves];
Keller a1706 [electromagnetic, decay of solutions].
@ Thermal properties: Lin ht/98-conf;
Ghezelbash & Mann JHEP(02)ht/01 [action, entropy, and dS-cft].
@ In other theories: Kodama & Arraut PTEP(14)-a1312 [in dRGT massive gravity theory, stability];
Addazi & Capozziello MPLA(16)-a1602 [in f(R) gravity]
@ Related topics: Podolský GRG(99)gq [extreme];
Nayak et al PRD(01)gq/00 [in Einstein universe];
Lake PRD(02)gq/01 [lensing];
Bytsenko & Goncharov IJMPA(02)gq [monopoles and Hawking radiation];
Zhang et al ChPL(12)-a0911 [tunneling to de Sitter space].
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