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Chin. Phys., 2007, Vol. 16(12): 3605-3609    DOI: 10.1088/1009-1963/16/12/009
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Supplement to the previous application of the first junction condition to a highly symmetric spacetime

Qin Yi-Ping
Center for Astrophysics, Guangzhou University, Guangzhou 510006, China National Astronomical Observatories/Yunnan Observatory, Chinese Academy of Sciences, Kunming 650011, China Physics Department, Guangxi University, Nanning 530004, China
Abstract  Application of the first junction condition to a highly symmetric spacetime was investigated recently in {\it Chin. Phys. Lett.} B {\bf 546} 189 2006, where a partial differential equation arising from the connection of the Robertson--Walker and the Schwarzschild--de Sitter metrics was presented, but no solutions of the equation were provided. Here we provide a proof to the statement that there exist solutions of the equation. In addition, an example of the solution and some analyses associated with this issue are presented. We find that in connecting the two metrics, there are three conditions which should be satisfied. Of these conditions, one condition constrains the place where the two metrics can take the same value for a local system whose mass is provided which marks the boundary of the system, and the other two constrain the transformation form. In realizing the connection of the two metrics, the latter two conditions are required to be satisfied only at the boundary defined by the former condition.
Keywords:  metrics      general relativity      junction conditions  
Published:  20 December 2007
PACS:  04.20.-q (Classical general relativity)  
Fund: Project supported by the National Science Fund for Distinguished Young Scholars (Grant No 10125313), the National Natural Science Foundation of China (Grant Nos 10573005 and 10273019), and the Fund for Top Scholars of Guangdong Province (Grant No Q02114)

Cite this article: 

Qin Yi-Ping Supplement to the previous application of the first junction condition to a highly symmetric spacetime 2007 Chin. Phys. 16 3605

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