The series solution to the metric of stationary vacuum with axisymmetry

doi:10.1088/1674-1056/19/3/030402

中国物理B ›› 2010, Vol. 19 ›› Issue (3): 30402-030402.doi: 10.1088/1674-1056/19/3/030402

The series solution to the metric of stationary vacuum with axisymmetry

辜英求

School of Mathematical Science, Fudan University, Shanghai 200433, China

收稿日期:2009-03-22 修回日期:2009-08-01 出版日期:2010-03-15 发布日期:2010-03-15

The series solution to the metric of stationary vacuum with axisymmetry

Gu Ying-Qiu(辜英求)^†

School of Mathematical Science, Fudan University, Shanghai 200433, China

Received:2009-03-22 Revised:2009-08-01 Online:2010-03-15 Published:2010-03-15

摘要/Abstract

摘要： The multipole moment method not only conduces to the understanding of the deformation of the space--time, but also serves as an effective tool to approximately solve the Einstein field equation with. However, the usual multipole moments are recursively determined by a sequence of symmetric and trace-free tensors, which is inconvenient for practical resolution. In this paper, we develop a simplified procedure to generate the series solutions to the metric of the stationary vacuum with axisymmetry, and show its validity. In order to understand the free parameters in the solution, we propose to take the Schwarzschild metric as a standard ruler, and some well- known examples are analysed and compared with the series solutions in detail.

Abstract: The multipole moment method not only conduces to the understanding of the deformation of the space--time, but also serves as an effective tool to approximately solve the Einstein field equation with. However, the usual multipole moments are recursively determined by a sequence of symmetric and trace-free tensors, which is inconvenient for practical resolution. In this paper, we develop a simplified procedure to generate the series solutions to the metric of the stationary vacuum with axisymmetry, and show its validity. In order to understand the free parameters in the solution, we propose to take the Schwarzschild metric as a standard ruler, and some well- known examples are analysed and compared with the series solutions in detail.

Key words: stationary metric, multipole moments, asymptotically flat, series solution

中图分类号: (Exact solutions)

04.20.Jb

04.20.Gz (Spacetime topology, causal structure, spinor structure)

辜英求. The series solution to the metric of stationary vacuum with axisymmetry[J]. 中国物理B, 2010, 19(3): 30402-030402.

Gu Ying-Qiu(辜英求). The series solution to the metric of stationary vacuum with axisymmetry[J]. Chin. Phys. B, 2010, 19(3): 30402-030402.

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The series solution to the metric of stationary vacuum with axisymmetry

The series solution to the metric of stationary vacuum with axisymmetry

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