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arXiv · 1909.07756

Spacetimes with all Penrose limits diagonalisable

Paul Tod
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Abstract

We consider the problem of finding all space-time metrics for which all plane-wave Penrose limits are diagonalisable plane waves. This requirement leads to a conformally invariant differential condition on the Weyl spinor which we analyse for different algebraic types in the Petrov-Pirani-Penrose classification. The only vacuum examples, apart from actual plane waves which are their own Penrose limit, are some of the nonrotating type D metrics, but some nonvacuum solutions are also identified. The condition requires the Weyl spinor, whenever it is nonzero, to be proportional to a valence-4 Killing spinor with a real function of proportionality.

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Paul Tod. 2019-09-17. Spacetimes with all Penrose limits diagonalisable. https://doi.org/10.1088/1361-6382%2Fab738a

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