Index Gymnastics

The technique of extracting the content from geometric (tensor) equations by working in component notation and rearranging indices as required. Index gymnastics is a fundamental component of special and general relativity (Misner et al. 1973, pp. 84-89). Examples of index gymnastics include

			(1)
			(2)
			(3)
			(4)
			(5)
			(6)
			(7)
			(8)

(Misner et al. 1973, p. 85), where is the metric tensor, is the Kronecker delta, is a comma derivative, is the antisymmetric tensor part, and is the symmetric tensor part.