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Asymptotically shear-free and twist-free null geodesic congruences

Carlos Kozameh1 and Ezra T Newman2

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The Robinson–Trautman spacetime is a special case of asymptotically flat spacetimes that possess asymptotically shear-free and twist-free (surface forming) null geodesic congruences. In this paper we show that, although they are rare, a larger class of asymptotically flat spacetimes with this property does exist. In particular, we display the class of spacetimes that possess this dual property and demonstrate how these congruences can be found. In addition, we show that in each case the congruence is isolated in the sense that there are no other neighbouring congruences with this dual property.


PACS

02.40.-k Geometry, differential geometry, and topology

04.20.Ha Asymptotic structure

MSC

83C30 Asymptotic procedures (radiation, news functions, H-spaces, etc.)

51F20 Congruence and orthogonality (See also 20H05)

Subjects

Mathematical physics

Gravitation and cosmology

Dates

Issue 11 (7 June 2007)

Received 20 March 2007, in final form 26 April 2007

Published 22 May 2007



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