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Initial data sets for Schwarzschild spacetime
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
School of Mathematical Sciences Queen Mary College, University of London.
2007 (English)In: Physical Review D. Particles and fields, ISSN 0556-2821, Vol. 75, 024027-024041 p.Article in journal (Refereed) Published
Abstract [en]

A characterization of initial data sets for the Schwarzschild spacetime is provided. This characterization is obtained by performing a 3+1 decomposition of a certain invariant characterization 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.

Place, publisher, year, edition, pages
2007. Vol. 75, 024027-024041 p.
Keyword [en]
General Relativity, Initial value problem
National Category
URN: urn:nbn:se:liu:diva-40917DOI: 10.1103/PhysRevD.75.024027Local ID: 54575OAI: diva2:261766
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2011-01-11

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Garcia-Parrado, Alfonso
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The Institute of TechnologyApplied Mathematics
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Physical Review D. Particles and fields

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