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arXiv · 0811.0449

The Series Solution to the Metric of Stationary Vacuum with Axisymmetry

Ying-Qiu Gu
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Abstract

The multipole moments method is not only an aid to understand the deformation of the space-time, but also an effective tool to solve the approximate solutions of the Einstein field equation. However, The usual multipole moments are recursively defined by a sequence of symmetric and trace-free tensors, which are inconvenient for practical resolution. In this paper, we develop a simple procedure to generate the series solutions, and propose a method to identify the free parameters by taking the Schwarzschild metric as a standard ruler. Some well known examples are analyzed and compared with the series solutions.

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Ying-Qiu Gu. 2008-11-04. The Series Solution to the Metric of Stationary Vacuum with Axisymmetry. https://doi.org/10.1088/1674-1056/19/3/030402

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