Schwarzschild-de Sitter Spacetime  

In General
* 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.
* 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.
@ Quantum: Nojiri & Odintsov PRD(99); Nojiri & Odintsov IJMPA(00)ht/99.
> Related topics: see perturbations, radiation, solutions of Einstein's equation.

Similar Metrics
* Nariai solution: A degenerate or extreme version of the Schwarzschild-de Sitter metric; A conformally non-flat, singularity-free perfect fluid expanding cosmological model, satisfying the weak energy condition.
@ Nariai: Dadhich gq/01; Ortaggio PRD(02)gq/01 [impulsive waves].
@ Perturbations: Yoshino et al PRD(04)gq [ < 0].

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) [complete analytic solution].
@ 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 20 jun 2008