Twisted Lorentzian manifolds, a characterization with torse-forming time-like unit vectors

TL;DR

This paper characterizes twisted Lorentzian manifolds using a unique torse-forming time-like vector field, extending previous characterizations of Robertson-Walker spacetimes to more general geometries with scale functions depending on space and time.

Contribution

It introduces a new characterization of twisted manifolds via a unique torse-forming time-like vector field without additional constraints, generalizing known spacetime models.

Findings

Characterization of twisted manifolds with a unique torse-forming vector field

Derivation of Ricci tensor for twisted manifolds

Connection to stress-energy tensor of an imperfect fluid

Abstract

Robertson-Walker and Generalized Robertson-Walker spacetimes may be characterized by the existence of a time-like unit torse-forming vector field, with other constrains. We show that Twisted manifolds may still be characterized by the existence of such (unique) vector field, with no other constrain. Twisted manifolds generalize RW and GRW spacetimes by admitting a scale function that depends both on time and space. We obtain the Ricci tensor, corresponding to the stress-energy tensor of an imperfect fluid.