A semi-symmetric metric connection, perfect fluid space-time and phantom barrier
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| Format: | Preprint |
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2025
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| _version_ | 1866911689680617472 |
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| author | Maksimović, Miroslav Zlatanović, Milan Najdanović, Marija |
| author_facet | Maksimović, Miroslav Zlatanović, Milan Najdanović, Marija |
| contents | We consider a concircularly semi-symmetric metric connection and its application. The Ricci tensors with respect to the concircularly semi-symmetric metric connection are symmetric, and they are used to define Einstein type manifolds. In this way, conditions under which a pseudo-Riemannian manifold is quasi-Einstein are obtained. On a Lorentzian manifold, a concircularly semi-symmetric metric connection with a unit timelike generator becomes a semi-symmetric metric $P$-connection, and a Lorentzian manifold becomes a GRW space-time. { It is proven in which case the scalar curvature of a perfect fluid space-time with that connection is constant and what its value is, which implies a reduction to Einstein manifold. } Furthermore, an application to the theory of relativity is presented, and the value of the equation of state is examined. It is ultimately shown that the equation of state in a perfect fluid space-time that satisfies Einstein field equation with cosmological constant and admits a unit timelike torse-forming vector represents a phantom barrier. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_00849 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A semi-symmetric metric connection, perfect fluid space-time and phantom barrier Maksimović, Miroslav Zlatanović, Milan Najdanović, Marija Differential Geometry General Relativity and Quantum Cosmology 53B05, 53B30, 53B50, 53C25, 83C05 We consider a concircularly semi-symmetric metric connection and its application. The Ricci tensors with respect to the concircularly semi-symmetric metric connection are symmetric, and they are used to define Einstein type manifolds. In this way, conditions under which a pseudo-Riemannian manifold is quasi-Einstein are obtained. On a Lorentzian manifold, a concircularly semi-symmetric metric connection with a unit timelike generator becomes a semi-symmetric metric $P$-connection, and a Lorentzian manifold becomes a GRW space-time. { It is proven in which case the scalar curvature of a perfect fluid space-time with that connection is constant and what its value is, which implies a reduction to Einstein manifold. } Furthermore, an application to the theory of relativity is presented, and the value of the equation of state is examined. It is ultimately shown that the equation of state in a perfect fluid space-time that satisfies Einstein field equation with cosmological constant and admits a unit timelike torse-forming vector represents a phantom barrier. |
| title | A semi-symmetric metric connection, perfect fluid space-time and phantom barrier |
| topic | Differential Geometry General Relativity and Quantum Cosmology 53B05, 53B30, 53B50, 53C25, 83C05 |
| url | https://arxiv.org/abs/2510.00849 |