On integrability of the Killing equation

被引:10
作者
Houri, Tsuyoshi [1 ]
Tomoda, Kentaro [1 ]
Yasui, Yukinori [2 ]
机构
[1] Kobe Univ, Dept Phys, 1-1 Rokkodai, Kobe, Hyogo 6578501, Japan
[2] Setsunan Univ, Fac Sci & Engn, 17-8 Ikeda Nakamachi, Neyagawa, Osaka 5728508, Japan
关键词
Killing tensor; integrable system; integrability condition; prolongation; Young symmetry; STRUCTURAL EQUATIONS; TENSORS; SYMMETRIES; INTEGRALS;
D O I
10.1088/1361-6382/aaa4e7
中图分类号
P1 [天文学];
学科分类号
0704 ;
摘要
Killing tensor fields have been thought of as describing the hidden symmetry of space(-time) since they are in one-to-one correspondence with polynomial first integrals of geodesic equations. Since many problems in classical mechanics can be formulated as geodesic problems in curved space and spacetime, solving the defining equation for Killing tensor fields (the Killing equation) is a powerful way to integrate equations of motion. Thus it has been desirable to formulate the integrability conditions of the Killing equation, which serve to determine the number of linearly independent solutions and also to restrict the possible forms of solutions tightly. In this paper, we show the prolongation for the Killing equation in a manner that uses Young symmetrizers. Using the prolonged equations, we provide the integrability conditions explicitly.
引用
收藏
页数:22
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