Characterizations of generalized Robertson-Walker spacetimes concerning gradient solitons

Krishnendu De; Mohammad Nazrul Islam Khan; Uday Chand De

doi:10.1016/j.heliyon.2024.e25702

Characterizations of generalized Robertson-Walker spacetimes concerning gradient solitons

Heliyon. 2024 Feb 6;10(4):e25702. doi: 10.1016/j.heliyon.2024.e25702. eCollection 2024 Feb 29.

Authors

Krishnendu De¹, Mohammad Nazrul Islam Khan², Uday Chand De³

Affiliations

¹ Department of Mathematics, Kabi Sukanta Mahavidyalaya, The University of Burdwan. Bhadreswar, Hooghly, West Bengal, India.
² Department of Computer Engineering, College of Computer, Qassim University, Buraydah, Saudi Arabia.
³ Department of Pure Mathematics, University of Calcutta, West Bengal, India.

Abstract

In this article, we examine gradient type Ricci solitons and $(m, τ)$ -quasi Einstein solitons in generalized Robertson-Walker (GRW) spacetimes. Besides, we demonstrate that in this scenario the GRW spacetime presents the Robertson-Walker (RW) spacetime and the perfect fluid (PF) spacetime presents the phantom era. Consequently, we show that if a GRW spacetime permits a gradient τ-Einstein solitons, then it also represents a PF spacetime under certain condition.

Keywords: 53C50; 53Z05; 83C05; Differential equations; Generalized Robertson-Walker spacetime; Gradient $(m, τ)$ -quasi Einstein soliton; Gradient Ricci soliton; Nonlinear equations; Partial differential equations.