Every tetrad uniquely determines the pseudo-Riemannian spacetime metric \(g_{ij}\). However, the converse does not hold since the tetrad has 16 independent components whereas the spacetime metric, \(g_{ij} = g_{ji}\), has only 10 independent components. The extra 6 degrees of freedom of the tetrads that are not determined by the metric may be represented by the elements of a 6-parameter internal Lorentz group. That is, the local tetrads are determined by the spacetime metric up to local Lorentz