Axisymmetric stationary solutions with arbitrary multipole moments
Thomas B\"ackdahl
TL;DR
This paper develops a method to construct axisymmetric stationary spacetimes from arbitrary multipole moments, using a convergence condition on a power series, enabling approximate solutions and term estimates.
Contribution
It introduces a new approach to generate solutions from specified multipole moments with convergence criteria and approximation capabilities.
Findings
Formulated a convergence condition for multipole moments
Provided a method for approximate solutions and term estimates
Enabled construction of axisymmetric stationary spacetimes from arbitrary 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.
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