A simple characterization of generalized Robertson-Walker spacetimes

TL;DR

This paper provides a simple characterization of generalized Robertson-Walker spacetimes by showing they are exactly Lorentzian manifolds admitting a timelike concircular vector field, extending classical results.

Contribution

It introduces a straightforward criterion for identifying generalized Robertson-Walker spacetimes based on the existence of a specific vector field.

Findings

Characterization of generalized Robertson-Walker spacetimes via timelike concircular vector fields

Extension of classical Robertson-Walker spacetime results

Simplified criteria for identifying these spacetimes

Abstract

A generalized Robertson-Walker spacetime is the warped product with base an open interval of the real line endowed with the opposite of its metric and base any Riemannian manifold. The family of generalized Robertson-Walker spacetimes widely extends the one of classical Robertson-Walker spacetimes. In this article we prove a very simple characterization of generalized Robertson-Walker spacetimes; namely, a Lorentzian manifold is a generalized Robertson-Walker spacetime if and only if it admits a timelike concircular vector field.