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arXiv · 2101.00856

On the geometry of Petrov type II spacetimes

Steffen Aksteiner·Lars Andersson·Bernardo Araneda·Bernard Whiting
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Abstract

In general, geometries of Petrov type II do not admit symmetries in terms of Killing vectors or spinors. We introduce a weaker form of Killing equations which do admit solutions. In particular, there is an analog of the Penrose-Walker Killing spinor. Some of its properties, including associated conservation laws, are discussed. Perturbations of Petrov type II Einstein geometries in terms of a complex scalar Debye potential yield complex solutions to the linearized Einstein equations. The complex linearized Weyl tensor is shown to be half Petrov type N. The remaining curvature component on the algebraically special side is reduced to a first order differential operator acting on the potential.

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Steffen Aksteiner, Lars Andersson, Bernardo Araneda, Bernard Whiting. 2021-01-04. On the geometry of Petrov type II spacetimes. https://doi.org/10.1088/1361-6382%2Fabf542

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