C-Metric  

In General
* Idea: A solution of Einstein-Maxwell theory, describing two oppositely charged black holes uniformly accelerating in opposite directions.
* Line element:

ds2 = A–2 (x+y)–2 [dy2/F(y) + dx2/G(x) + k–2G(x) dφ2k2A2F(y) dt2] ,

where F(y) = –1 + y2 – 2mAy3 + e2A2y4; G(x) = 1 – x2 – 2mAx3e2A2x4 = –F(–x); m, e and A are parameters, and k is a constant whose value is fixed by regularity conditions on the metric.

References
@ Discovery: Levi-Civita RAL(17); Newman & Tamburino JMP(61).
@ General references: Kinnersley & Walker PRD(70); Ehlers & Kundt in(72) [name]; Ashtekar & Dray CMP(81); Dray GRG(82); Bonnor CQG(90); Hong & Teo CQG(03) [new form]; Bini et al PRD(04)gq [perturbations, gravitational Stark effect].
@ Geodesics: Bini et al CQG(05)-a1408 [in the equatorial plane]; > s.a. types of geodesics.
@ Properties: Ernst JMP(76) [singularity and removal]; Sládek & Finley CQG(10) [asymptotic properties].
@ Matter: Bini et al CQG(15)-a1509 [massless Dirac particles].
@ Interpretation: Cornish & Uttley GRG(95) [vacuum], GRG(95) [charged]; Emparan PLB(96)ht, NPB(97)ht/96 [string-motivated]; Pravda & Pravdová gq/02-in; Griffiths et al CQG(06)gq.

Related Metrics > s.a. Bonnor-Swaminarayan; Melvin Solution.
@ In de Sitter space, with cosmological constant: Podolský & Griffiths PRD(01)gq/00; Dias & Lemos PRD(03); Salti APS(05)gq [energy]; Chen et al PRD(15)-a1501.
@ Rotating: Hong & Teo CQG(05) [new form]; Griffiths & Podolský CQG(05)gq; Bini et al JMP(08)-a1408 [massless field perturbations].
@ Other generalizations: Podolský & Griffiths GRG(01)gq/00 [null limit, unbounded acceleration]; Podolský CzJP(02)gq [in anti-de Sitter spacetime]; Dias & Lemos PRD(03)ht [extremal limits]; Willeman & Beke PRD(10)-a1001 [expanding perfect fluids].


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