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Commun. Korean Math. Soc. 2023; 38(1): 235-242
Online first article September 20, 2022 Printed January 31, 2023
https://doi.org/10.4134/CKMS.c220044
Copyright © The Korean Mathematical Society.
Ricci $\rho$-soliton in a perfect fluid spacetime with a gradient vector field
Dibakar Dey, Pradip Majhi
Kolkata - 700019; Kolkata - 700019
In this paper, we studied several geometrical aspects of a perfect fluid spacetime admitting a Ricci $\rho$-soliton and an $\eta$-Ricci $\rho$-soliton. Beside this, we consider the velocity vector of the perfect fluid space time as a gradient vector and obtain some Poisson equations satisfied by the potential function of the gradient solitons.
Keywords: Ricci $\rho$-soliton, $\eta$-Ricci $\rho$-soliton, perfect fluid spacetime, Poisson equation, geodesics
MSC numbers: 53B50, 53C44, 53C50, 83C02
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