Approach to a Cauchy Problem in Stability Study of the Schwarzschild Black Hole

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 insuftlcient for the stability study.     

Ground State Eigenfunction of Spheroidal Wave Functions

We study the spin-weighted spheroidal wave functions in the case of s = m = 0. Their eigenvalue problem is investigated by the perturbation method in supersymmetric quantum mechanics. In the first three terms of parameter a = a^2 w^2, the ground eigenvalue and eigenfunction are obtained. The obtained ground eigenfunction is elegantly in dosed forms. These results are new and very useful for the application of the spheroidal wave functions.     

MOCVD反应器热流场的数值模拟研究

本文以低压、旋转、垂直喷淋结构的MOCVD反应器为对象,应用二维数学模型分析与计算,对反应器内部的质量输运过程进行了比较详细的研究与讨论.通过计算发现:在一定范围内,增加进气流量Q、降低操作压力P、设定适宜的生长温度t、保持合理的基座转速ω等,不仅可以非常有效地抑制热浮力效应,同时也使衬底表面流体的流动速度进一步增加,从而实现反应器内部的流场和温度场的均匀分布.研究的结果,不仅为高品质的外延生长提供了有效的解决方案,而且也为MOCVD反应器的优化设计提供了重要的参考依据.     

A New Model For the Double Well Potential

A new model for the double well potential is presented. In the new potential, the exchanging rate could be easily calculated by the perturbation method in supersymmetric quantum mechanics. It gives good results whether the barrier is high or sallow. The new model has many merits and may be used in the double well problem.     

Stability problem in Rindler 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.