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Chin. Phys. B, 2010, Vol. 19(3): 030402    DOI: 10.1088/1674-1056/19/3/030402
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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
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.
Keywords:  stationary metric      multipole moments      asymptotically flat      series solution  
Received:  22 March 2009      Revised:  01 August 2009      Accepted manuscript online: 
PACS:  04.20.Jb (Exact solutions)  
  04.20.Gz (Spacetime topology, causal structure, spinor structure)  

Cite this article: 

Gu Ying-Qiu(辜英求) The series solution to the metric of stationary vacuum with axisymmetry 2010 Chin. Phys. B 19 030402

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