Wu–Sprung potential

2013-04-22T00:03:59Z

70.192.84.95: Correct spelling "interpretate" to "interpret"

The '''Plebanski tensor''' is a [[tensor rank|rank 4 tensor]] in [[general relativity]] constructed from the [[trace-free Ricci tensor]]. It was first defined by [[Jerzy Plebański]] in 1964.<ref>{{citation|first1=J.|last1=Plebański|title=|journal=Acta Phys. Polon.|volume=26|page=963|year=1964}}</ref>

Let <math>S_{ab}</math> be the trace-free Ricci tensor:

:<math>S_{ab}=R_{ab}-\frac{1}{4}Rg_{ab}.</math>

Then the Plebanski tensor is defined as

:<math>P^{ab}{}_{cd}=S^{[a}{}_{[c}S^{b]}{}_{d]}+\delta^{[a}{}_{[c}S^{b]e}S_{d]e}-\frac{1}{6}\delta^{[a}{}_{[c}\delta^{b]}{}_{d]}S^{ef}S_{ef}.</math>

The advantage of the Plebanski tensor is that it shares the same symmetries as the [[Weyl tensor]]. It therefore becomes possible to classify different [[spacetime]]s based on additional algebraic symmetries of the Plebanski tensor in a manner analogous to the [[Petrov classification]].<ref>{{citation|first1=C. B. G.|last1=McIntosh|first2=J. M.|last2=Foyster|first3=A. W.-C.|last3=Lun|title=The classification of the Ricci and Plebanski tensors in general relativity using Newman-Penrose formalism|journal=J. Math. Phys.|volume=22|page=2620|year=1981|doi=10.1063/1.524840|bibcode = 1981JMP....22.2620M }}</ref>

==References==
<references/>

[[Category:Tensors]]

{{relativity-stub}}

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Wu–Sprung potential