中国物理B ›› 2007, Vol. 16 ›› Issue (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

覃一平   

  1. 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
  • 出版日期:2007-12-20 发布日期:2007-12-20
  • 基金资助:
    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)

Supplement to the previous application of the first junction condition to a highly symmetric spacetime

Qin Yi-Ping(覃一平)   

  1. Center for Astrophysics, Guangzhou University, Guangzhou 510006, China; National Astronomical Observatories/Yunnan Observatory, Chinese Academy of Sciences, Kunming 650011, ChinaPhysics Department, Guangxi University, Nanning 530004, China
  • Online:2007-12-20 Published:2007-12-20
  • Supported by:
    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)

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摘要： 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.

关键词: general relativity, metrics, junction conditions

Abstract: Application of the first junction condition to a highly symmetric spacetime was investigated recently in Chin. Phys. Lett. B 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.

Key words: general relativity, metrics, junction conditions

中图分类号:  (Classical general relativity)

  • 04.20.-q