A simple characterization of generalized Robertson-Walker spacetimes
General Relativity and Quantum Cosmology
2015-06-23 v1 Differential Geometry
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.
Keywords
Cite
@article{arxiv.1411.0270,
title = {A simple characterization of generalized Robertson-Walker spacetimes},
author = {Bang-Yen Chen},
journal= {arXiv preprint arXiv:1411.0270},
year = {2015}
}
Comments
5 pages, to appear in General Relativity and Gravitation