Axisymmetric stationary solutions with arbitrary multipole moments

Abstract

In this paper, the problem of finding an axisymmetric stationary spacetime from a specified set of multipole moments, is studied. The condition on the multipole moments, for existence of a solution, is formulated as a convergence condition on a power series formed from the multipole moments. The methods in this paper can also be used to give approximate solutions to any order as well as estimates on each term of the resulting power series.

12 pages

References in corpus (3)

• Explicit multipole moments of stationary axisymmetric spacetimes
• Static axisymmetric space-times with prescribed multipole moments
• Calculation of, and bounds for, the multipole moments of stationary spacetimes

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