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arXiv · 1707.05201

Analysis of a Bianchi-like equation satisfied by the Mars-Simon tensor

Florian Beyer·Tim-Torben Paetz
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Abstract

The Mars-Simon tensor (MST), which e.g. plays a crucial role to provide gauge invariant characterizations of the Kerr-NUT-(A)(dS) family, satisfies a Bianchi-like equation. In this paper we analyze this equation in close analogy to the Bianchi equation, in particular it will be shown that the constraints are preserved supposing that a generalized Buchdahl condition holds. This permits the systematic construction of solutions to this equation in terms of a well-posed Cauchy problem. A particular emphasis lies on the asymptotic Cauchy problem, where data are prescribed on a spacelike scri (i.e. for $\Lambda >0$). In contrast to the Bianchi equation, the MST equation is of Fuchsian type at scri, for which existence and uniqueness results are derived.

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Florian Beyer, Tim-Torben Paetz. 2017-07-17. Analysis of a Bianchi-like equation satisfied by the Mars-Simon tensor. https://doi.org/10.1063/1.4996700

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