Perfect fluid spacetimes and gradient solitons
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866910314761551872 |
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| author | De, Krishnendu De Uday Chand Syied, Abdallah Abdelhameed Turki, Nasser Bin Alsaeed, Suliman |
| author_facet | De, Krishnendu De Uday Chand Syied, Abdallah Abdelhameed Turki, Nasser Bin Alsaeed, Suliman |
| contents | This article deals with the investigation of perfect fluid spacetimes endowed with concircular vector field. It is shown that in a perfect fluid spacetime with concircular vector field, the velocity vector field annihilates the conformal curvature tensor and in dimension 4, a perfect fluid spacetime is a generalized Robertson-Walker spacetime with Einstein fibre. Moreover, we prove that if a perfect fluid spacetime equipped with concircular vector field admits a second order symmetric parallel tensor, then either the state equation of the perfect fluid spacetime is characterized by $p=\frac{3-n}{n-1}σ$ , or the tensor is a constant multiple of the metric tensor. We also characterize the perfect fluid spacetimes with concircular vector field whose Lorentzian metrics are Ricci soliton, gradient Ricci soliton, gradient Yamabe solitons and gradient $m$-quasi Einstein solitons, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2105_03149 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Perfect fluid spacetimes and gradient solitons De, Krishnendu De Uday Chand Syied, Abdallah Abdelhameed Turki, Nasser Bin Alsaeed, Suliman General Relativity and Quantum Cosmology Differential Geometry 53C50, 53E20, 53C35, 53E40 This article deals with the investigation of perfect fluid spacetimes endowed with concircular vector field. It is shown that in a perfect fluid spacetime with concircular vector field, the velocity vector field annihilates the conformal curvature tensor and in dimension 4, a perfect fluid spacetime is a generalized Robertson-Walker spacetime with Einstein fibre. Moreover, we prove that if a perfect fluid spacetime equipped with concircular vector field admits a second order symmetric parallel tensor, then either the state equation of the perfect fluid spacetime is characterized by $p=\frac{3-n}{n-1}σ$ , or the tensor is a constant multiple of the metric tensor. We also characterize the perfect fluid spacetimes with concircular vector field whose Lorentzian metrics are Ricci soliton, gradient Ricci soliton, gradient Yamabe solitons and gradient $m$-quasi Einstein solitons, respectively. |
| title | Perfect fluid spacetimes and gradient solitons |
| topic | General Relativity and Quantum Cosmology Differential Geometry 53C50, 53E20, 53C35, 53E40 |
| url | https://arxiv.org/abs/2105.03149 |