Investigating string cloud spacetimes with energy-momentum tensor constraints in general relativity

Sunil Kumar Yadav; Sameh Shenawy; Nasser Bin Turki; Yanlin Li; Sunil Kumar Yadav; Sameh Shenawy; Nasser Bin Turki; Yanlin Li

doi:10.3934/math.2025955

AIMS Mathematics

2025, Volume 10, Issue 9: 21492-21511. doi: 10.3934/math.2025955

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Research article

Investigating string cloud spacetimes with energy-momentum tensor constraints in general relativity

1.
Department of Applied Science and Humanities, United College of Engineering & Research, UPSIDC, Industrial Area, Naini, Prayagraj, Uttar Predesh, India
2.
Basic Science Department, Modern Academy for Engineering and Technology, Maadi, Egypt
3.
Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
4.
School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China

Received: 07 January 2025 Revised: 23 August 2025 Accepted: 08 September 2025 Published: 17 September 2025
MSC : 53B30, 53C25, 53C44, 53C50, 53C80

The objective of this study was to investigate the behavior of relativistic G(QE)$ _{n} $ string cloud spacetime endowed with various forms of the string cloud energy-momentum tensor $ \mathcal{T} $, which includes the string cloud fluid density $ \alpha $ and string tension $ \beta $. A G(QE)$ _{n} $ string cloud spacetime with a covariantly constant energy-momentum tensor satisfies the equation of state $ \frac{\alpha}{\beta} = -1 $, and represents either a massive string cloud spacetime or a bulk viscous fluid spacetime. Moreover, when a string cloud spacetime is coupled with a covariantly constant energy-momentum tensor, the equation of state $ \frac{\alpha}{\beta} = -1 $ coincides with the state equation for a cloud of geometric strings or represents the quintessence era. G(QE)$ _{n} $ string cloud spacetimes with Codazzi-type and pseudo-symmetric energy-momentum tensors were investigated. Furthermore, we characterized $ \mathcal{T} $-recurrent, weakly $ \mathcal{T} $-symmetric, specially weakly $ \mathcal{T} $-symmetric, generalized $ \mathcal{T} $-recurrent, semi-generalized $ \mathcal{T} $-recurrent, and quadratic Killing-type energy-momentum tensors on a string cloud spacetime with a Killing velocity vector field, and concluded that the string cloud spacetime either represents a massive string cloud spacetime or corresponds to the quintessence era.
Citation: Sunil Kumar Yadav, Sameh Shenawy, Nasser Bin Turki, Yanlin Li. Investigating string cloud spacetimes with energy-momentum tensor constraints in general relativity[J]. AIMS Mathematics, 2025, 10(9): 21492-21511. doi: 10.3934/math.2025955

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Abstract

The objective of this study was to investigate the behavior of relativistic G(QE)$ _{n} $ string cloud spacetime endowed with various forms of the string cloud energy-momentum tensor $ \mathcal{T} $, which includes the string cloud fluid density $ \alpha $ and string tension $ \beta $. A G(QE)$ _{n} $ string cloud spacetime with a covariantly constant energy-momentum tensor satisfies the equation of state $ \frac{\alpha}{\beta} = -1 $, and represents either a massive string cloud spacetime or a bulk viscous fluid spacetime. Moreover, when a string cloud spacetime is coupled with a covariantly constant energy-momentum tensor, the equation of state $ \frac{\alpha}{\beta} = -1 $ coincides with the state equation for a cloud of geometric strings or represents the quintessence era. G(QE)$ _{n} $ string cloud spacetimes with Codazzi-type and pseudo-symmetric energy-momentum tensors were investigated. Furthermore, we characterized $ \mathcal{T} $-recurrent, weakly $ \mathcal{T} $-symmetric, specially weakly $ \mathcal{T} $-symmetric, generalized $ \mathcal{T} $-recurrent, semi-generalized $ \mathcal{T} $-recurrent, and quadratic Killing-type energy-momentum tensors on a string cloud spacetime with a Killing velocity vector field, and concluded that the string cloud spacetime either represents a massive string cloud spacetime or corresponds to the quintessence era.

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