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from Part II - Solutions with groups of motions
Published online by Cambridge University Press: 10 November 2009
Introduction
In this chapter we give solutions containing a perfect fluid (other than the Λ-term, treated in §13.3) and admitting an isometry group transitive on spacelike orbits S3. By Theorem 13.2 the relevant metrics are all included in (13.1) with ε = –1, k = 1, and (13.20).
The properties of these metrics and their implications as cosmological models are beyond the scope of this book, and we refer the reader to standard texts, which deal principally with the Robertson–Walker metrics (12.9) (e.g. Weinberg (1972), Peacock (1999), Bergstrom and Goobar (1999), Liddle and Lyth (2000)), and to the reviews cited in §13.2. Solutions containing both fluid and magnetic field are of cosmological interest, and exact solutions have been given by many authors, e.g. Doroshkevich (1965), Shikin (1966), Thorne (1967) and Jacobs (1969). Details of these solutions are omitted here, but they frequently contain, as special cases, solutions for fluid without a Maxwell field. Similarly, they and the fluid solutions may contain as special cases the Einstein–Maxwell and vacuum fields given in Chapter 13.
There is an especially close connection between vacuum or Einstein– Maxwell solutions and corresponding solutions with a stiff perfect fluid (equation of state p = μ) or equivalently a massless scalar field.
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