Stability problem in Rindler spacetime

The stability problem of the Rindler spacetime is carefullystudies by using the scalar wave perturbation. Using two differentcoordinate systems, the scalar wave equation is investigated. Theresults are different in the two cases. They are analysed andcompared with each other in detail. The following conclusions areobtained: (a) the Rindler spacetime as a whole is not stable; (b) theRindler spacetime can exist stably only as part of the Minkowskispacetime, and the Minkowski spacetime can be a real entityindependently; (c) there are some defects for the scalar waveequation written by the Rindler coordinates, and it is unsuitable forthe investigation of the stability properties of the Rindlerspacetime. All these results may shed some light on the stabilityproperties of the Schwarzschild black hole. It is natural andreasonable for one to infer that: (a) perhaps the Regge--Wheelerequation is not sufficient to determine the stable properties; (b) the Schwarzschild black hole as a wholemight be really unstable; (c) the Kruskal spacetime is stable and canexist as a real physical entity; whereas the Schwarzschild black holecan occur only as part of the Kruskal spacetime.