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The search for the generating compatibility conditions (CC) of a given operator is a very recent problem met in general relativity in order to study the Killing operator for various standard useful metrics. Accordingly, this paper can be considered as a natural continuation of a previous paper recently published in JMP under the title Minkowski, Schwarschild and Kerr metrics revisited. In particular, we prove that the intrinsic link existing between the lack of formal exactness of an operator sequence on the jet level, the lack of formal exactness of its corresponding symbol sequence and the lack of formal integrability (FI) of the initial operator is of a purely homological nature as it is based on the long exact connecting sequence provided by the so-called snake lemma in homological algebra. It is therefore quite difficult to grasp it in general and even more difficult to use it on explicit examples. It does not seem that any one of the results presented in this paper is known as most of the other authors who studied the above problem of computing the total number of generating CC are confusing this number with the degree of generality introduced by A. Einstein in his 1930 letters to E. Cartan. One of the motivating examples that we provide is so striking that it is even difficult to imagine that such an example could exist. We hope this paper could be used as a source of testing examples for future applications of computer algebra in general relativity and, more generally, in mathematical physics.
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篇名 Generating Compatibility Conditions and General Relativity
来源期刊 现代物理(英文) 学科 数学
关键词 FORMAL Theory of SYSTEMS of Partial DIFFERENTIAL Equations Compatibility Conditions ACYCLICITY FORMAL Integrability Involutivity DIFFERENTIAL SEQUENCE JANET SEQUENCE Spencer SEQUENCE General Relativity Killing SYSTEMS
年,卷(期) xdwlyw_2019,(3) 所属期刊栏目
研究方向 页码范围 371-401
页数 31页 分类号 O1
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研究主题发展历程
节点文献
FORMAL
Theory
of
SYSTEMS
of
Partial
DIFFERENTIAL
Equations
Compatibility
Conditions
ACYCLICITY
FORMAL
Integrability
Involutivity
DIFFERENTIAL
SEQUENCE
JANET
SEQUENCE
Spencer
SEQUENCE
General
Relativity
Killing
SYSTEMS
研究起点
研究来源
研究分支
研究去脉
引文网络交叉学科
相关学者/机构
期刊影响力
现代物理(英文)
月刊
2153-1196
武汉市江夏区汤逊湖北路38号光谷总部空间
出版文献量(篇)
1826
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0
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