Approach to a Cauchy Problem in Stability Study of the Schwarzschild Black Hole
TIAN Gui-Hua 1,2, WANG Shi-Kun, ZHONG Shu-Quan
School of Science, Beijing University of Posts and Telecommunications, Beijing 100876Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080
Approach to a Cauchy Problem in Stability Study of the Schwarzschild Black Hole
TIAN Gui-Hua 1,2;WANG Shi-Kun;ZHONG Shu-Quan
School of Science, Beijing University of Posts and Telecommunications, Beijing 100876Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080
摘要Generally, the Schwarzschild black hole is proven to be stable by two different methods: the mode-decomposition method and the integral method. We show that the integral method can only apply to the initial data vanishing at both the horizon and the spatial infinity. It can not treat the initial data only vanishing at the spatial infinity. We give an example to show the misleading information caused by the use of tortoise coordinates in the perturbation equations. Subsequently, the perturbation equations in the Schwarzschild coordinates are shown to be insufficient for the stability study.
Abstract：Generally, the Schwarzschild black hole is proven to be stable by two different methods: the mode-decomposition method and the integral method. We show that the integral method can only apply to the initial data vanishing at both the horizon and the spatial infinity. It can not treat the initial data only vanishing at the spatial infinity. We give an example to show the misleading information caused by the use of tortoise coordinates in the perturbation equations. Subsequently, the perturbation equations in the Schwarzschild coordinates are shown to be insufficient for the stability study.
(Late stages of stellar evolution (including black holes))
引用本文:
TIAN Gui-Hua;WANG Shi-Kun;ZHONG Shu-Quan. Approach to a Cauchy Problem in Stability Study of the Schwarzschild Black Hole[J]. 中国物理快报, 2007, 24(6): 1475-1478.
TIAN Gui-Hua, WANG Shi-Kun, ZHONG Shu-Quan. Approach to a Cauchy Problem in Stability Study of the Schwarzschild Black Hole. Chin. Phys. Lett., 2007, 24(6): 1475-1478.
[1] Tian G H, Wang Sh K and Zhao Zh 2005 arxiv:gr-qc0504055 [2] Tian G H 2006 Chin. Phys. Lett. 23 783 [3] Tian G H 2005 arxiv: gr-qc0512101 [4] Tian G H, Wang S K and Zhao Z 2006 Chin. Phys. 151430 or arxiv: gr-qc0509030 [5] Vishveshwara C 1970 Phys. Rev. D 1 2870 [6] Chandrasekhar S 1983 The Mathematical Theory of BlackHole (Oxford: Oxford University Press) p 199 [7] Wald R M 1979 J. Math. Phys. 20 1056 [8] Kay B S and Wald R M 1987 Class. Quantum Grav. 4 893 [9] Tian G H, Wang Sh K and Zhong Sh Q 2006 arxiv:gr-qc0603113 [10] He T M and Wang Y J 2005 Chin. Phys. Lett. 22 773 [11] Liu D J and Li X Z 2005 Chin. Phys. Lett. 22 1600 [12] Tian G H, Wang S K and Zhong S Q 2006 arxiv: gr-qc0603040
2007, Vol. 24 
