Geometrization of string cloud spacetime in general relativity

Mohd Danish Siddiqi; Meraj Ali Khan; Ibrahim Al-Dayel; Khalid Masood; Mohd Danish Siddiqi; Meraj Ali Khan; Ibrahim Al-Dayel; Khalid Masood

doi:10.3934/math.20231487

AIMS Mathematics

2023, Volume 8, Issue 12: 29042-29057. doi: 10.3934/math.20231487

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Research article

Geometrization of string cloud spacetime in general relativity

1.
Department of Mathematics College of Science, Jazan University, P. O. Box 277, Jazan 45142, Saudi Arabia
2.
Department of Mathematics and Statistics College of Science Imam Mohammad Ibn Saud Islamic University, P. O. Box-65892, Riyadh 11566, Saudi Arabia

Received: 03 September 2023 Revised: 30 September 2023 Accepted: 11 October 2023 Published: 26 October 2023
MSC : 53B30, 53C44, 53C50, 53C80

The purpose of the article is to analyze the behavior of spacetime using a string cloud energy-momentum tensor $ \mathcal{T} $ having string cloud fluid density $ \rho $ and string tension $ \lambda $, named relativistic string cloud spacetime. We obtain some results for string cloud spacetime with a divergence-free matter tensor and a diminishing space matter tensor. Next, we discuss some curvature characteristics, such as conformally flat, Ricci semi-symmetric and pseudo-Ricci-symmetric, for relativistic string cloud spacetime. In addition, we gain a condition that coincides with the equation of state for the cloud of geometric strings in Ricci semi-symmetric string cloud spacetime.
- Lorentzian spacetime manifold,
- Einstein's field equation,
- string cloud energy momentum tensor,
- curvatures,
- geomtric strings
Citation: Mohd Danish Siddiqi, Meraj Ali Khan, Ibrahim Al-Dayel, Khalid Masood. Geometrization of string cloud spacetime in general relativity[J]. AIMS Mathematics, 2023, 8(12): 29042-29057. doi: 10.3934/math.20231487

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Abstract

The purpose of the article is to analyze the behavior of spacetime using a string cloud energy-momentum tensor $ \mathcal{T} $ having string cloud fluid density $ \rho $ and string tension $ \lambda $, named relativistic string cloud spacetime. We obtain some results for string cloud spacetime with a divergence-free matter tensor and a diminishing space matter tensor. Next, we discuss some curvature characteristics, such as conformally flat, Ricci semi-symmetric and pseudo-Ricci-symmetric, for relativistic string cloud spacetime. In addition, we gain a condition that coincides with the equation of state for the cloud of geometric strings in Ricci semi-symmetric string cloud spacetime.

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