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Summary

We describe the Petrov classification of spacetimes, by the number of independent principal null directions (PNDs), eigenvectors of the Weyl tensor. The Petrov types are defined, and they are described in the Newman–Penrose formalism. Finally, examples of the various Petrov type metrics are given.

Summary

We describe the Newman–Penrose formalism for gravity in four dimensions. We first define some relations for covariant derivatives, then define some basis vectors and the spin coefficients, for the spin connection in this basis. Then commutation relations and the transport relations for basis vectors, and the Newman–Penrose field equations, for the action of covariant derivatives on spin coefficients. We then show how we can change null frames, and the important case of the spinorial notation for the Newman–Penrose formalism. Finally, we describe some applications of the formalism.

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31 - The Petrov classification

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30 - The Newman–Penrose formalism

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2 results

31 - The Petrov classification

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30 - The Newman–Penrose formalism

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