Static axisymmetric spacetimes with prescribed multipole moments

In this paper we develop a method of finding the static axisymmetric spacetime corresponding to any given set ofmultipolemoments. 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 Ger...

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Bibliographic Details
Published inClassical and quantum gravity Vol. 22; no. 9; pp. 1607 - 1621
Main Authors Bäckdahl, Thomas, Herberthson, Magnus
Format Journal Article
LanguageEnglish
Published Bristol IOP Publishing 07.05.2005
Institute of Physics
Subjects
algebraic equation
axisymmetric
Exact sciences and technology
exact solution
General relativity and gravitation
MATEMATIK
MATHEMATICS
multipole moments
Physics
spacetime
static
Multipoles
Space-time
Monopoles
Quadrupoles
Power series
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Summary:In this paper we develop a method of finding the static axisymmetric spacetime corresponding to any given set ofmultipolemoments. 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 spacetime for any given set of multipole moments subject to a (specified) convergence criterion. We also use this method to confirm a conjecture of Hernández-Pastora and Martín concerning the monopole–quadrupole solution.
ISSN:0264-9381
1361-6382
1361-6382
DOI:10.1088/0264-9381/22/9/009