Tian Gui-Hua(田贵花)a)b)†, Wang Shi-Kun(王世坤)b), and Zhong Shu-Quan(钟树泉)a)
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
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.
Received: 02 November 2006
Revised: 15 March 2007
Accepted manuscript online:
Fund: 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.
Cite this article:
Tian Gui-Hua(田贵花), Wang Shi-Kun(王世坤), and Zhong Shu-Quan(钟树泉) Stability problem in Rindler spacetime 2007 Chinese Physics 16 2889
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