Vector-tetrads and the creation of matter

Abstract

The possibility is examined of using a tetrad vector field to provide field relations that admit the creation of matter. Except for additive terms in certain auxiliary tensors depending on only first derivatives of the field, it is shown that a tetrad field determines two and only two linearly independent tensors corresponding in complexity to the single Ricci tensor of Riemannian geometry. It is suggested that combinations of these tensors might serve as the Einstein tensor and the ‘creation tensor’ in F. Hoyle’s proposed modification of Einstein’s field relations. Certain tetrad fields discovered by H. P. Robertson and A. G. Walker are shown to conform to the cosmological principle in a required sense. Using these in field relations of the suggested form, equations for cosmological models are obtained. One such model closely resembles that derived by Hoyle. So far as they go, the indications obtained in the paper are that tetrad fields may be appropriate for the further mathematical study of the possibility of continuous creation.