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Characterizations of perfect fluid spacetimes obeying $f (ℛ)$ -gravity equipped with different gradient solitons

Department of Mathematics, Kabi Sukanta Mahavidyalaya, The University of Burdwan, Bhadreswar, P. O.-Angus, Hooghly, 712221 West Bengal, India

E-mail Address: krishnendu.de@outlook.in

Corresponding author.

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Young Jin Suh

Department of Mathematics and RIRCM, Kyungpook National University, Daegu 41566, South Korea

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

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, and

Uday Chand De

Department of Mathematics, University of Calcutta, West Bengal, India

E-mail Address: uc_de@yahoo.com

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https://doi.org/10.1142/S0219887823501748Cited by:2 (Source: Crossref)

Abstract

The prime object of this paper is to study the perfect fluid spacetimes obeying $f (ℛ)$ -gravity, when $η$ -Ricci solitons, gradient $η$ -Ricci solitons, gradient Einstein solitons and gradient $m$ -quasi Einstein solitons are its metrics. At first, the existence of the $η$ -Ricci solitons is proved by a non-trivial example. We establish conditions for which the $η$ -Ricci solitons are expanding, steady or shrinking. Besides, in the perfect fluid spacetimes obeying $f (ℛ)$ -gravity, when the potential vector field of $η$ -Ricci soliton is of gradient type, we acquire a Poisson equation. Moreover, we investigate gradient $η$ -Ricci solitons, gradient Einstein solitons and gradient $m$ -quasi Einstein solitons in $f (ℛ)$ -gravity, respectively. As a result, we establish some significant theorems about dark matter era.

Keywords:

AMSC: 83C05, 83D05, 53C50

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