Characterizations of Perfect fluid spacetimes obeying $f(\mathcal{R})$-gravity equipped with different gradient solitons
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909090398076928 |
|---|---|
| author | Suh, Krishnendu De Young Jin De, Uday Chand |
| author_facet | Suh, Krishnendu De Young Jin De, Uday Chand |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_03254 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Characterizations of Perfect fluid spacetimes obeying $f(\mathcal{R})$-gravity equipped with different gradient solitons Suh, Krishnendu De Young Jin De, Uday Chand Differential Geometry Mathematical Physics 83C05, 83D05, 53C50 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. |
| title | Characterizations of Perfect fluid spacetimes obeying $f(\mathcal{R})$-gravity equipped with different gradient solitons |
| topic | Differential Geometry Mathematical Physics 83C05, 83D05, 53C50 |
| url | https://arxiv.org/abs/2202.03254 |