A geometric invariant characterising initial data for the Kerr-Newman spacetime
Abstract
We describe the construction of a geometric invariant characterising initial data for the Kerr-Newman spacetime. This geometric invariant vanishes if and only if the initial data set corresponds to exact Kerr-Newman initial data, and so characterises this type of data. We first illustrate the characterisation of the Kerr-Newman spacetime in terms of Killing spinors. The space spinor formalism is then used to obtain a set of four independent conditions on an initial Cauchy hypersurface that guarantee the existence of a Killing spinor on the development of the initial data. Following a similar analysis in the vacuum case, we study the properties of solutions to the approximate Killing spinor equation and use them to construct the geometric invariant.
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Cite
@article{arxiv.1609.05129,
title = {A geometric invariant characterising initial data for the Kerr-Newman spacetime},
author = {Michael J. Cole and Juan A. Valiente Kroon},
journal= {arXiv preprint arXiv:1609.05129},
year = {2018}
}
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34 pages