Sufficient conditions for a Lorentzian manifold to be a generalized Robertson-Walker spacetime

Abstract

The aim of this article is to find the conditions under which a Lorentzian manifold to be a generalized Robertson-Walker spacetime. We illustrate that a Lorentzian manifold admitting a semi-symmetric metric connection represents a generalized Robertson-Walker spacetime under certain restrictions on the Ricci tensor and torsion tensor. As a consequence, we establish that such a manifold becomes a static spacetime.