A note on extended Lorentzian recurrent manifolds

TL;DR

This paper revisits extended Lorentzian recurrent manifolds, revealing their conformal flatness, quasi-constant curvature, and their equivalence to perfect fluid Robertson-Walker space-times, providing specific models under certain conditions.

Contribution

It demonstrates that extended recurrent Lorentzian manifolds with a time-like covector are equivalent to Robertson-Walker space-times and derives related physical models.

Findings

Manifold is conformally flat.

Manifold has quasi-constant curvature.

Models for incoherent radiation are obtained.

Abstract

Extended recurrent pseudo-Riemannian manifolds were introduced by Mileva Prvanovic'. We reconsider her work in the light of recent results and show that the manifold is conformally flat, and it is a space of quasi-constant curvature. We also show that an extended recurrent Lorentzian manifold, with time-like associated covector, is a perfect fluid Robertson-Walker space-time. We obtain the equation of state; in n = 4 and if the scalar curvature is zero, a model for incoherent radiation is obtained.