Curvature invariant (general relativity) | Wikipedia audio article
Channel: wikipedia tts
Date: 25/12/2018

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Curvature_invariant_(general_relativity)


00:00:38 1 Principal invariants
00:04:17 1.1 Relation with Ricci decomposition
00:05:51 1.2 Relation with Bel decomposition
00:08:53 1.3 Expression in Newman–Penrose formalism
00:10:27 2 Distinguishing Lorentzian manifolds
00:11:34 3 See also



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SUMMARY
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In general relativity,  curvature invariants are a set of scalars formed from the Riemann, Weyl and Ricci tensors - which represent curvature, hence the name, - and possibly operations on them such as contraction, covariant differentiation and dualisation.
Certain invariants formed from these curvature tensors play an important role in classifying spacetimes. Invariants are actually less powerful for distinguishing locally non-isometric Lorentzian manifolds than they are for distinguishing Riemannian manifolds. This means that they are more limited in their applications than for manifolds endowed with a positive definite metric tensor.