Schwarzschild-de
Sitter Spacetime| Schwarzschild-de
Sitter Spacetime |
In General > s.a. solutions of
einstein's equation.
* Idea: The natural generalization
of the Schwarzschild metric to the case of nonzero cosmological constant 
;
Also called Kottler
Solution.
* Line element: Replace
1 – (2 GM/r) 
1 – (2 GM/r) – ( r2/3)
in the Schwarzschild line element.
* Extreme case: The
parameters satisfy 9(GM)2 =
1 (in four spacetime dimensions).
Thermodynamics > s.a. black-hole
thermodynamics; black-hole radiation.
* Temperature:
In d dimensions, the temperature is given by
T = (d–3) (rH 
2rH)
/ 4
,
where the upper (lower) sign holds
in the Anti-de Sitter (de Sitter) case.
@ General references: Brown
et al PRD(94);
Teitelboim ht/02-in
[and stability]; Bolen & Cavaglià GRG(05)gq/04 [and
gup].
@ 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 a0810 [two approaches].
@ Quantum: Nojiri & Odintsov PRD(99);
Nojiri & Odintsov IJMPA(00)ht/99.
Perturbations > s.a. perturbations
of schwarzschild spacetime.
@ References: Yoshino et al PRD(04)gq [ < 0].
Similar Metrics
* 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 a0902 [generalized, positive cosmological constant].
@ Other modified metrics: Wang et al CQG(09)
[quantum deformed].
References > s.a. tests
of general relativity with light.
@ General: Kottler AdP(18).
@ Geometry, coordinates: Kamimura et al MPLA(91)
[connection formulation]; Lake CQG(06)gq/05 [maximal
extension].
@
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),
PRD(08)
[complete analytic solution]; Dymnikova et al G&C(08) [overview].
@ Other classical matter: Islam PLA(83) [planet and light motion].
@ 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].
@ Thermal properties:
Lin ht/98-in;
Ghezelbash & Mann JHEP(02)ht/01 [action,
entropy, and dS-cft].
@ Other topics: Podolsky 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].
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send feedback and suggestions to bombelli at olemiss.edu – modified 28
apr 2009