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

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.

6 pages, marginal errors corrected, reference updated

References in corpus (3)

• A simple characterization of generalized Robertson-Walker spacetimes
• Generalized Robertson-Walker space times, a survey
• On the Weyl and Ricci tensors of Generalized Robertson-Walker space-times

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