Penrose limits of homogeneous spaces

Details Penrose limits of homogeneous spaces Penrose limits of homogeneous spaces

2004-05-26

arxiv.org/abs/math/0405506v2

J.Geom.Phys. 56 (2006) 1516-1533

Mathematics

Differential Geometry

16 pages, many changes particularly to sections 6 and 7

Scientific paper

We prove that the Penrose limit of a spacetime along a homogeneous geodesic is a homogeneous plane wave spacetime and that the Penrose limit of a reductive homogeneous spacetime along a homogeneous geodesic is a Cahen--Wallach space. We then consider several homogenous examples to show that these results are indeed sharp and conclude with a remark about the existence of null homogeneous geodesics.

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