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arxiv: gr-qc/0502012 · v1 · submitted 2005-02-03 · 🌀 gr-qc

Static axisymmetric space-times with prescribed multipole moments

classification 🌀 gr-qc
keywords momentsmultipolestaticaxisymmetricgivenmethodsolutionspace-time
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In this article we develop a method of finding the static axisymmetric space-time corresponding to any given set of multipole moments. In addition to an implicit algebraic form for the general solution, we also give a power series expression for all finite sets of multipole moments. As conjectured by Geroch we prove in the special case of axisymmetry, that there is a static space-time for any given set of multipole moments subject to a (specified) convergence criterion. We also use this method to confirm a conjecture of Hernandez-Pastora and Martin concerning the monopole-quadropole solution.

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