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Static axisymmetric space-times with prescribed multipole moments

Thomas Backdahl·Magnus Herberthson
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Abstract

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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Thomas Backdahl, Magnus Herberthson. 2005-02-03. Static axisymmetric space-times with prescribed multipole moments. https://doi.org/10.1088/0264-9381%2F22%2F9%2F009

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