Static axisymmetric spacetimes with prescribed multipole moments

Thomas Bäckdahl, Magnus Herberthson
2005 Classical and quantum gravity  
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
more » ... so use this method to confirm a conjecture of Hernandez-Pastora and Martin concerning the monopole-quadropole solution.
doi:10.1088/0264-9381/22/9/009 fatcat:ksbjo65vubasjo3iar6jhysbha