Algebraic and differential Rainich conditions for symmetric trace-free tensors of higher rank
Algebraic and differential Rainich conditions for symmetric trace-free tensors of higher rank
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高阶对称无迹张量的代数和微分Rainich条件
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
P. Lankinen
中科院分区：
文献类型：
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作者：
G. Bergqvist;P. Lankinen
我们提出了对称和无迹张量 T 的类 Rainich 条件的研究。对于任意偶数阶，我们找到张量满足无源场方程的充要微分条件。对于秩 4，在一般情况下，我们将这些条件与先前获得的代数条件相结合，以获得 T 上的完整代数和微分条件，使其成为 Weyl 候选张量的超能张量，满足 Bianchi 真空方程。根据贝尔和塞克雷斯的结果，这意味着在真空中，一般来说，T 必须是时空的贝尔-罗宾逊张量。对于等级 3 的情况，我们推导了 T 成为无质量自旋 3/2 场的超能张量的完整必要代数和微分条件，满足无源场方程。
We present a study of Rainich-like conditions for symmetric and trace-free tensors T. For arbitrary even rank we find a necessary and sufficient differential condition for a tensor to satisfy the source-free field equation. For rank 4, in a generic case, we combine these conditions with previously obtained algebraic conditions to gain a complete set of algebraic and differential conditions on T for it to be a superenergy tensor of a Weyl candidate tensor, satisfying the Bianchi vacuum equations. By a result of Bell and Szekeres, this implies that in vacuum, generically, T must be the Bel–Robinson tensor of the spacetime. For the rank 3 case, we derive a complete set of necessary algebraic and differential conditions for T to be the superenergy tensor of a massless spin-3/2 field, satisfying the source-free field equation.