A Mathematical Comparison of the Schwarzschild and Kerr Metrics

作     者：J.-F. Pommaret J.-F. Pommaret

作者机构：CERMICS Ecole des Ponts ParisTech Paris France 

出 版 物：《Journal of Modern Physics》 (现代物理（英文）)

年 卷 期：2020年第11卷第10期

页      面：1672-1710页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Formal Integrability Involutivity Compatibility Condition Janet Sequence Spencer Sequence Minkowski Metric Schwarzschild Metric Kerr Metric 

摘      要：A few physicists have recently constructed the generating compatibility conditions (CC) of the Killing operator for the Minkowski (M), Schwarzschild (S) and Kerr (K) metrics. They discovered second order CC, well known for M, but also third order CC for S and K. In a recent paper (DOI:10.4236/jmp.2018.910125) we have studied the cases of M and S, without using specific technical tools such as Teukolski scalars or Killing-Yano tensors. However, even if S(m) and K(m, a) are depending on constant parameters in such a way that S → M when m → 0 and K→ S when a → 0, the CC of S do not provide the CC of M when m → 0 while the CC of K do not provide the CC of S when a → 0. In this paper, using tricky motivating examples of operators with constant or variable parameters, we explain why the CC are depending on the choice of the parameters. In particular, the only purely intrinsic objects that can be defined, namely the extension modules, may change drastically. As the algebroid bracket is compatible with the