2003
DOI: 10.1088/0264-9381/20/24/004
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Vacuum type I spacetimes and aligned Papapetrou fields: symmetries

Abstract: Abstract. We analyze type I vacuum solutions admitting an isometry whose Killing 2-form is aligned with a principal bivector of the Weyl tensor, and we show that these solutions belong to a family of type I metrics which admit a group G 3 of isometries. We give a classification of this family and we study the Bianchi type for each class. The classes compatible with an aligned Killing 2-form are also determined. The SzekeresBrans theorem is extended to non vacuum spacetimes with vanishing Cotton tensor.

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Cited by 8 publications
(20 citation statements)
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“…We can quote some examples of non radiative fields: (i) All the type D vacuum solutions are known [20,21]. (ii) A result inferred by Szekeres [22] and confirmed by Brans [23] states that no vacuum solutions of type IM ∞ exist (see [25] for a generalization).…”
Section: Propositionmentioning
confidence: 99%
“…We can quote some examples of non radiative fields: (i) All the type D vacuum solutions are known [20,21]. (ii) A result inferred by Szekeres [22] and confirmed by Brans [23] states that no vacuum solutions of type IM ∞ exist (see [25] for a generalization).…”
Section: Propositionmentioning
confidence: 99%
“…In the second case φ = φ(t) and then Eq. (25) implies that b(ρ) = 0 if, and only if, b(ω) = 0, and then proposition 12 applies and the spacetime admits a Killing vector which is parallel to b. In the first case, for metrics of class I, the spacetime is a FLRW universe as a consequence of lemma 12 in Appendix B.…”
Section: E Classes Defined By Invariants Associated With the Energy mentioning
confidence: 94%
“…12 Some of the conditions on the Killing 2-form imposed in the literature quoted above could be very restrictive. Thus, in a previous paper 13 we have shown that the Petrov type I vacuum spacetimes admitting an isometry whose Killing 2-form is aligned with a Weyl principal bivector belong to two classes of metrics which admit a 3-dimensional group of isometries of Bianchi type I or II. In the present work we show that a close relation between the Weyl principal directions and the isometry group exists in these classes.…”
Section: Introductionmentioning
confidence: 94%
“…So, we can take ν 2 = ν 3 = 0 in the second structure equations (13). Taking into account the definition of ν i from (14) we obtain…”
Section: Vacuum Solutions Of Class I 12mentioning
confidence: 99%
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