  We carefully study the stable problem of the Rindler space time by the scalar
wave perturbation. Using the two different coordinate systems, the scalar wave
equation is investigated. The results are different in these two cases. They
are analyzed and compared in detail. The conclusions are: (a) the Rindler space
time as a whole is not stable; (b) the Rindler space time could exist stably
only as a part of the Minkowski space time, and the Minkowski space time could
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
investigation of the stable properties of the Rindler space time. All these
results might shed some lights on the stable properties of the Schwarzschild
black hole. It is natural and not unreasonable for one to infer that: (a)
perhaps the Regge-Wheeler equation is not sufficient to decide the stable
properties; (b) the Schwarzschild black hole as a whole might be really
unstable; (c) the Kruskal space time is stable and can exist as a real physical
entity ; whereas the Schwarzschild black hole could occur only as part of the
Kruskal space time.
