The stable problem in the Rindler space-time

TL;DR

This paper investigates the stability of Rindler space-time using scalar wave perturbations, revealing that it is unstable as a whole but stable as part of Minkowski space, and discusses implications for black hole stability.

Contribution

It provides a detailed analysis of the stability of Rindler space-time in different coordinate systems and discusses the implications for black hole stability theories.

Findings

Rindler space-time is not stable as a whole.

Rindler space-time can be stable only as part of Minkowski space.

Scalar wave equations in Rindler coordinates have defects.

Abstract

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.