Dimensionally dependent identities

Abstract

In the general theory of relativity a number of apparently unrelated identities peculiar to a 4-dimensional space are frequently used. However, the proofs usually presented appear to have no common ideas and, furthermore, it is not clear at what stage the dimensionality restriction plays a significant role. In this note a technique is presented which explicitly exhibits the dimensionality dependence and thereby enables the above identities to be generalized for n-dimensional spaces. It is also shown that the above identities are all special cases of a more general identity valid for n = 4.