在纽曼彭罗斯形式主义中寻找积分和恒等式：对类的评论。量子重力26（2009）105022和Gen. Relativ.重力（2014）46：1703
Finding integrals and identities in the Newman Penrose formalism: a comment on Class. Quantum Grav. 26 (2009) 105022 and on Gen. Relativ. Gravit. (2014)46:1703
摘要：
在1969年金纳斯利，使用NP形式主义，发现所有的彼得罗夫型D，利玛窦单位，解决了爱因斯坦的场方程。然而，在这样做-因为它似乎-他忽略了两个基本身份（或约束）的四个NP变量和嘉当不变量以及，即$τ\barτ-π\barπ=0$和$ρ\barμ-μ\barρ=0$。从那时起，这些身份一直被忽视或证明在特殊情况下（如electrovac解决方案）。直到2009年，埃德加等人通过扩展使用GHP形式主义和计算机代数系统，才成功地证明了这些恒等式。在这篇参考文献中，它是-而间接地-暗示，正在考虑的结果是证明只有在GHP形式主义，因此后者是最佳的工具，对不变的分类和研究类的解决方案的EFE。2014年，J.J. Ferrando & J.A.赛斯使用张量代数（2-形式），没有援助的CAS，作者证明了所需的结果，他们提供了一个更精细和扩展的分类彼得罗夫型D，里奇平坦，解决方案。当有人读到第三部作品时，尽管它很美，概念也很简单，但人们会觉得作者事先就知道他们想证明什么，而事实并非总是如此。本短篇作品的目的是通过具体的例子（即，类的Ricci平坦，彼得罗夫D型几何），原来的NP形式主义，视为外部微分系统足以提供所需的结果-因此评论第二次引用的文件-不仅没有（原则上）的援助，一个CAS，但也获得一个新的进一步（未知至今）积分的EDS -因此评论第三次引用的文件。
英文摘要：
In 1969 Kinnersley, using the NP formalism, found all the Petrov type D, Ricci flat, solutions to the Einstein's Field Equations. Yet, in doing so -as it seems- he neglected two fundamental identities (or constraints) on four NP variables and Cartan invariants as well, namely $τ\barτ-π\barπ=0$ and $ρ\barμ-μ\barρ=0$. Since then, these identities have been constantly either overlooked or proven under special circumstances (e.g. electrovac solutions). It was only until 2009 when Edgar et al. by making an extended use of the GHP formalism, and of a computer algebra system, succeeded in proving those identities in the general case. In that reference, it was -rather indirectly- implied that the results under consideration were provable only within the GHP formalism and thus the latter is the optimal tool towards the invariant classification and study of classes of solutions to the EFEs. In 2014 there was a kind of response to that paper by J.J. Ferrando & J.A. Saez. Using the tensorial algebra (of 2-forms), and without the aid of a CAS, the authors proved the desired result and they offer a much more refined and extended classification of the Petrov type D, Ricci flat, solutions. Never the less when someone reads that third work, although beautiful and conceptually simple, one has the feeling that the authors know in advance what they want to prove; something which is not always the case. The goal of the present short work is to prove, through the specific example (i.e., the class of Ricci flat, Petrov type D geometries), that the original NP formalism, seen as an exterior differential system suffices to provide the desired results -thus commenting on the second cited paper- not only without (in principle) the aid of a CAS, but also to obtain a new further (unknown until now) integral of the EDS -thus commenting on the third cited paper.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
