中国物理B ›› 2007, Vol. 16 ›› Issue (10): 2889-2893.doi: 10.1088/1009-1963/16/10/011

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Stability problem in Rindler spacetime

王世坤1, 钟树泉2, 田贵花3   

  1. (1)Key Laboratory of Mathematics Mechanization, Academy of Mathematics and System Science, Chinese Academy of Sciences, Beijing 100080, China; (2)School of Science, Beijing University of Posts and Telecommunications. Beijing 100876, China; (3)School of Science, Beijing University of Posts and Telecommunications. Beijing 100876, China；Key Laboratory of Mathematics Mechanization, Academy of Mathematics and System Science, Chinese Academy of Sciences, Beijing 100080, China
  • 收稿日期:2006-11-02 修回日期:2007-03-15 出版日期:2007-10-08 发布日期:2007-10-08
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos~10475013, 10375087 and 10373003), the National Basic Research Program (Grant No~2004CB318000) and National Science Foundation for Post-Doctoral Scientists of China.

Stability problem in Rindler spacetime

Tian Gui-Hua(田贵花)a)b)†, Wang Shi-Kun(王世坤)b), and Zhong Shu-Quan(钟树泉)a)   

  1. a School of Science, Beijing University of Posts and Telecommunications. Beijing 100876, China; b Key Laboratory of Mathematics Mechanization, Academy of Mathematics and System Science, Chinese Academy of Sciences, Beijing 100080, China
  • Received:2006-11-02 Revised:2007-03-15 Online:2007-10-08 Published:2007-10-08
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos~10475013, 10375087 and 10373003), the National Basic Research Program (Grant No~2004CB318000) and National Science Foundation for Post-Doctoral Scientists of China.

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摘要： The stability problem of the Rindler spacetime is carefully studies by using the scalar wave perturbation. Using two different coordinate systems, the scalar wave equation is investigated. The results are different in the two cases. They are analysed and compared with each other in detail. The following conclusions are obtained: (a) the Rindler spacetime as a whole is not stable; (b) the Rindler spacetime can exist stably only as part of the Minkowski spacetime, and the Minkowski spacetime can be a real entity independently; (c) there are some defects for the scalar wave equation written by the Rindler coordinates, and it is unsuitable for the investigation of the stability properties of the Rindler spacetime. All these results may shed some light on the stability properties of the Schwarzschild black hole. It is natural and reasonable for one to infer that: (a) perhaps the Regge--Wheeler equation is not sufficient to determine the stable properties; (b) the Schwarzschild black hole as a whole might be really unstable; (c) the Kruskal spacetime is stable and can exist as a real physical entity; whereas the Schwarzschild black hole can occur only as part of the Kruskal spacetime.

关键词: stable problem, Rindler spacetime, Regge-Wheeler equation

Abstract: The stability problem of the Rindler spacetime is carefully studies by using the scalar wave perturbation. Using two different coordinate systems, the scalar wave equation is investigated. The results are different in the two cases. They are analysed and compared with each other in detail. The following conclusions are obtained: (a) the Rindler spacetime as a whole is not stable; (b) the Rindler spacetime can exist stably only as part of the Minkowski spacetime, and the Minkowski spacetime can be a real entity independently; (c) there are some defects for the scalar wave equation written by the Rindler coordinates, and it is unsuitable for the investigation of the stability properties of the Rindler spacetime. All these results may shed some light on the stability properties of the Schwarzschild black hole. It is natural and reasonable for one to infer that: (a) perhaps the Regge--Wheeler equation is not sufficient to determine the stable properties; (b) the Schwarzschild black hole as a whole might be really unstable; (c) the Kruskal spacetime is stable and can exist as a real physical entity; whereas the Schwarzschild black hole can occur only as part of the Kruskal spacetime.

Key words: stable problem, Rindler spacetime, Regge-Wheeler equation

中图分类号:  (Physics of black holes)

  • 04.70.-s
04.20.-q (Classical general relativity) 97.60.Lf (Black holes)