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All spacetimes with vanishing curvature invariants

V Pravda1, A Pravdová1, A Coley2 and R Milson2

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All Lorentzian spacetimes with vanishing invariants constructed from the Riemann tensor and its covariant derivatives are determined. A subclass of the Kundt spacetimes results and we display the corresponding metrics in local coordinates. Some potential applications of these spacetimes are discussed.


PACS

02.40.Ky Riemannian geometries

04.20.Jb Exact solutions

MSC

53B21 Methods of Riemannian geometry

83C15 Exact solutions

53B30 Lorentz metrics, indefinite metrics

Subjects

Mathematical physics

Gravitation and cosmology

Dates

Issue 23 (7 December 2002)

Received 14 August 2002, in final form 10 October 2002

Published 14 November 2002



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