Characterizations of twisted spacetimes

Twisted spacetimes generalize Robertson-Walker cosmological models by allowing the scale factor to depend on both spatial position and time, thereby modeling inhomogeneous cosmic expansion. This article establishes geometric conditions under which a Lorentzian manifold becomes a twisted spacetime and determines when such spacetimes reduce to homogeneous generalized Robertson-Walker (GRW) models. We prove that Lorentzian manifolds admitting semi-symmetric metric connections with covariantly constant torsion tensor possess twisted spacetime structure. A spacetime with quasi-constant curvature becomes twisted under a natural condition on the gradients of its defining curvature scalars. We demonstrate that a twisted spacetime reduces to a GRW spacetime if and only if the difference between the two scalar functions occurring in its Ricci decomposition is an eigenvalue of the Ricci tensor with respect to the generating time-like vector, and that Ricci-symmetric twisted spacetimes are necessarily GRW. Conformally flat twisted spacetimes are shown to be a special subclass of generalized quasi-Einstein manifolds or a perfect fluid spacetime, reducing to GRW under specific conditions, including Ricci recurrence. These results identify geometric constraints distinguishing inhomogeneous from homogeneous cosmological models. Finally, we construct some physically relevant cosmological metric of twisted form that verifies our results.