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Initial data sets for the Schwarzschild spacetime

Alfonso García-Parrado Gómez-Lobo·Juan A. Valiente Kroon
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Abstract

A characterisation of initial data sets for the Schwarzschild spacetime is provided. This characterisation is obtained by performing a 3+1 decomposition of a certain invariant characterisation of the Schwarzschild spacetime given in terms of concomitants of the Weyl tensor. This procedure renders a set of necessary conditions --which can be written in terms of the electric and magnetic parts of the Weyl tensor and their concomitants-- for an initial data set to be a Schwarzschild initial data set. Our approach also provides a formula for a static Killing initial data set candidate --a KID candidate. Sufficient conditions for an initial data set to be a Schwarzschild initial data set are obtained by supplementing the necessary conditions with the requirement that the initial data set possesses a stationary Killing initial data set of the form given by our KID candidate. Thus, we obtain an algorithmic procedure of checking whether a given initial data set is Schwarzschildean or not.

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Alfonso García-Parrado Gómez-Lobo, Juan A. Valiente Kroon. 2006-12-21. Initial data sets for the Schwarzschild spacetime. https://doi.org/10.1103/physrevd.75.024027

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