Some Properties of Empty Space-Time
Ezra Ted Newman · Journal of Mathematical Physics · 1961
In close analogy to the ``vierbein'' technique of representing world vectors as linear combinations of four fixed vectors, we have constructed from six linearly independent bivectors a (complete) set, or basis, of ten tensors of rank 4 that possess all the algebraic properties of the empty-space Riemann-Christoffel tensor (i.e., Weyl's tensor). Any actual Weyl tensor must be a linear combination of these ten; the expansion coefficients with respect to a given basis are uniquely determined. We have examined Petrov's classification scheme in terms of this formalism and have developed a further division into subclasses. Finally, we shall present in this paper, as an application of our technique, the derivation of plane-fronted waves.