The Series Solution to the Metric of Stationary Vacuum with Axisymmetry

Details The Series Solution to the Metric of Stationary Vacuum with Axisymmetry The Series Solution to the Metric of Stationary Vacuum with Axisymmetry

2008-11-04

arxiv.org/abs/0811.0449v3

Chinese Phys. B 19 030402 (2010)

Physics

General Physics

18 pages, no figure

Scientific paper

10.1088/1674-1056/19/3/030402

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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