Stability problem in Rindler spacetime  

作　　者：田贵花 王世坤 钟树泉 

机构地区：[1]School of Science, Beijing University of Posts and Telecommunications. Beijing 100876, China [2]Key Laboratory of Mathematics Mechanization, Academy of Mathematics and System Science, Chinese Academy of Sciences, Beijing 100080, China

出　　处：《Chinese Physics B》2007年第10期2889-2893,共5页中国物理B（英文版）

基　　金：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.

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.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 

分 类 号：O412.1[理学—理论物理]