Static axisymmetric space-times with prescribed multipole moments

Details Static axisymmetric space-times with prescribed multipole moments Static axisymmetric space-times with prescribed multipole moments

2005-02-03

arxiv.org/abs/gr-qc/0502012v1

Class.Quant.Grav. 22 (2005) 1607-1621

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

14 pages

Scientific paper

10.1088/0264-9381/22/9/009

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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