Expansion tensor in a modified de Sitter metric

Dragi Radojević

Theoretical and applied mechanics, Tome 8 (1982) no. 1, p. 119

Résumé

De Sitter's cosmological model was published in 1917. In that model, the density of matter is equal to zero, and that is why it is a model of "empty" space. On the occasion of that model, Einstein hinted at the possibility that matter is distributed on one sphere. That idea was implemented by V. K. Maljcev and M. A. Markov sixty years later [1]. In this paper, the expansion tensor in the modified de Sitter metric is examined. The expansion tensor is defined as \[ ǎrtheta_{lpha\beta}=\mathfrak L_\xi(g_{lpha\beta}+\xi_lpha\xi_\beta) \] where $\xi_\alpha$ is a time-type unit vector, $g_{\alpha\beta}$ is the metric tensor of the observed space, and $\mathfrak L_\xi$ is the derivative of Li. In relation to a suitably chosen coordinate system, there are conditions that determine positive expansion.