Lorentzian spacetimes with constant curvature invariants in four dimensions

Details Lorentzian spacetimes with constant curvature invariants in four dimensions Lorentzian spacetimes with constant curvature invariants in four dimensions

2009-04-30

arxiv.org/abs/0904.4877v1

Class.Quant.Grav.26:125011,2009

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

20pages, CQG accepted

Scientific paper

10.1088/0264-9381/26/12/125011

In this paper we investigate four dimensional Lorentzian spacetimes with constant curvature invariants ($CSI$ spacetimes). We prove that if a four dimensional spacetime is $CSI$, then either the spacetime is locally homogeneous or the spacetime is a Kundt spacetime for which there exists a frame such that the positive boost weight components of all curvature tensors vanish and the boost weight zero components are all constant. We discuss some of the properties of the Kundt-$CSI$ spacetimes and their applications. In particular, we discuss $\mathcal{I}$-symmetric spaces and degenerate Kundt $CSI$ spacetimes.

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