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arXiv · 1610.09527

Classification of the traceless Ricci tensor in 4-dimensional pseudo-Riemannian spaces of neutral signature

Adam Chudecki
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Abstract

The traceless Ricci tensor $C_{ab}$ in 4-dimensional pseudo-Riemannian spaces equipped with the metric of the neutral signature is analyzed. Its algebraic classification is given. This classification uses the properties of $C_{ab}$ treated as a matrix. The Petrov-Penrose types of Pleba\'nski spinors associated with the traceless Ricci tensor are given. Finally, the classification is compared with a similar classification in the complex case.

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Adam Chudecki. 2016-10-29. Classification of the traceless Ricci tensor in 4-dimensional pseudo-Riemannian spaces of neutral signature. https://doi.org/10.5506/aphyspolb.48.53

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