- Lanczos tensor
There are two different
tensor s sometime referred to as the Lanczos tensor (both named afterCornelius Lanczos ):* A tensor in the theory of
quadratic Lagrangian s, which vanishes infour dimensions .
* Thepotential tensor "H" for theWeyl tensor "C", this can be expressed as::C_{abcd}=H_{abc;d}-H_{abd;c}+H_{cda;b}-H_{cdb;a},::g_{ac}(H_{bd}+H_{db})-g_{ad}(H_{bc}+H_{cb})+ g_{bd}(H_{ac}+H_{ca})-g_{bc}(H_{ad}+H_{da}))/2,::2H^{ef}_{;;;e;f}(g_{ac}g_{bd}-g_{ad}g_{bc})/3,,
where the Lanczos tensor has the symmetries:H_{abc}+H_{bac}=0,,:H_{abc}+H_{bca}+H_{cab}=0,,and where H_{bd} is defined by:H_{bd} stackrel{mathrm{def{=} H^{~e}_{b;;d;e}-H^{~e}_{b;;e;d};.
Thus, the Lanczos potential tensor is a
gravitational field analog ofthevector potential "A" for theelectromagnetic field .External links
* [http://www.arXiv.org/abs/hep-th/gr-qc/9904006 gr-qc/9904006]
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