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23 April 2024
 
  » arxiv » 1707.5201

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Analysis of a Bianchi-like equation satisfied by the Mars-Simon tensor
Florian Beyer ; Tim-Torben Paetz ;
Date 17 Jul 2017
AbstractThe 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.
Source arXiv, 1707.5201
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