论文标题
完美流体空间的特征遵守$ f（\ Mathcal {r}）$ - 配备了不同梯度孤子的重力
Characterizations of Perfect fluid spacetimes obeying $f(\mathcal{R})$-gravity equipped with different gradient solitons
论文作者
论文摘要
本文的主要目的是研究$ f（\ Mathcal {r}）$ - 重力的完美流体空间，当$η$ -RRICCI solitons，渐变$η$ -RRICCI Solitons，渐变的Einstein solitons和渐变Einstein solitons和渐变$ M $ -QuM $ -quasi -quasi einstein solitons是其量子。首先，$η$ -RICCI唯一的存在是通过非平凡的例子证明的。我们建立了$η$ -RICCI唯一的范围正在扩展，稳定或收缩的条件。此外，在完美的流体空间中，请遵守$ f（\ Mathcal {r}）$ - 重力，当$η$ -Rricci soliton的潜在向量场是梯度类型时，我们获得了泊松方程。此外，我们研究了分别在$ f（\ Mathcal {r}）$ GREATITY中调查梯度$η$η$η$ -Ricrci soliton，Einstein solitons和渐变$ m $ -quasi Einstein solitons。结果，我们建立了一些有关暗物质时代的重要定理。
The prime object of this article is to study the perfect fluid spacetimes obeying $f(\mathcal{R})$-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 $f(\mathcal{R})$-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 $f(\mathcal{R})$-gravity, respectively. As a result, we establish some significant theorems about dark matter era.
