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arXiv · 1912.02809

Nil-Killing vector fields and type III deformations

Matthew Aadne
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Abstract

This paper is concerned with deformations of Kundt metrics in the direction of type $III$ tensors and nil-Killing vector fields whose flows give rise to such deformations. We find various characterizations within the Kundt class in terms of nil-Killing vector fields and obtain a theorem classifying algebraic stability of tensors, which has an application in finding sufficient criteria for a type $III$ deformation of the metric to preserve spi's. This is used in order to specify Lie algebras of nil-Killing vector fields that preserve the spi's, for degenerate Kundt metrics. Using this we discuss the characterization of Kundt-CSI spacetimes in terms of nil-Killing vector fields.

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Matthew Aadne. 2019-12-05. Nil-Killing vector fields and type III deformations. https://doi.org/10.1063/5.0018773

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