中国物理B ›› 2006, Vol. 15 ›› Issue (7): 1430-1434.doi: 10.1088/1009-1963/15/7/008

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Restudy of the stability problem of the Schwarzschild black hole

赵峥1, 王世坤2, 田贵花3   

  1. (1)Department of Physics, Beijing Normal University, Beijing 100875, China; (2)Key Laboratory of Mathematics Mechanization, Academy of Mathematics and System Science, Chinese Academy of Sciences, Beijing 100080, 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:2006-01-26 修回日期:2006-04-03 出版日期:2006-07-20 发布日期:2006-07-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10475013, 10373003 and 10375087), the National Basic Research Program (Grant No 2004CB318000) and the Post-Doctor Foundation of China.

Restudy of the stability problem of the Schwarzschild black hole

Tian Gui-Hua (田贵花)ab, Wang Shi-Kun (王世坤)b, Zhao Zheng (赵峥)c    

  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; c Department of Physics, Beijing Normal University, Beijing 100875, China
  • Received:2006-01-26 Revised:2006-04-03 Online:2006-07-20 Published:2006-07-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10475013, 10373003 and 10375087), the National Basic Research Program (Grant No 2004CB318000) and the Post-Doctor Foundation of China.

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摘要： The stability of the Schwarzschild black hole is restudied in the Painlevé coordinates. Using the Painlevé time coordinate to define the initial time, we reconsider the odd perturbation and find that the Schwarzschild black hole in the Painlevé coordinates is unstable. The Painlevé metric in this paper corresponds to the white-hole-connected region of the Schwarzschild black hole (r>2m) and the odd perturbation may be regarded as the angular perturbation. Therefore, the white-hole-connected region of the Schwarzschild black hole is unstable with respect to the rotating perturbation.

关键词: Schwarzschild black hole, angular perturbation, white-hole-connected region of the Schwarzschild black hole (r>2m)

Abstract: The stability of the Schwarzschild black hole is restudied in the Painlevé coordinates. Using the Painlevé time coordinate to define the initial time, we reconsider the odd perturbation and find that the Schwarzschild black hole in the Painlevé coordinates is unstable. The Painlevé metric in this paper corresponds to the white-hole-connected region of the Schwarzschild black hole ($r>2$ m) and the odd perturbation may be regarded as the angular perturbation. Therefore, the white-hole-connected region of the Schwarzschild black hole is unstable with respect to the rotating perturbation.

Key words: Schwarzschild black hole, angular perturbation, white-hole-connected region of the Schwarzschild black hole ($r>2$m)

中图分类号:  (Physics of black holes)

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