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A note on generalized Robertson–Walker space-times

Carlo Alberto Mantica

Physics Department, Università Degli Studi di Milano, Via Celoria 16, 20133 Milano, Italy

I. I. S. Lagrange, Via L., Modignani 65, 20161 Milano, Italy

E-mail Address: carloalberto.mantica@libero.it

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Young Jin Suh

Department of Mathematics, Kyungpook National University, Taegu 702-701, Korea

E-mail Address: yjsuh@knu.ac.kr

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, and

Uday Chand De

Department of Pure Mathematics, University of Calcutta, 35, Ballygunge Circular Road, Kolkatta-700019, West Bengal, India

E-mail Address: uc_de@yahoo.com

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https://doi.org/10.1142/S0219887816500791Cited by:49 (Source: Crossref)

Abstract

A generalized Robertson–Walker (GRW) space-time is the generalization of the classical Robertson–Walker space-time. In the present paper, we show that a Ricci simple manifold with vanishing divergence of the conformal curvature tensor admits a proper concircular vector field and it is necessarily a GRW space-time. Further, we show that a stiff matter perfect fluid space-time or a mass-less scalar field with time-like gradient and with divergence-free Weyl tensor are GRW space-times.

Keywords:

AMSC: 53C25, 53C35, 83F20

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