Riemann solitons on perfect fluid within $ f ({r}, {T^{2}}) $-gravity

Wedad A Alharbi; Shahroud Azami; Mehdi Jafari; Abdul Haseeb; Wedad A Alharbi; Shahroud Azami; Mehdi Jafari; Abdul Haseeb

doi:10.3934/math.20251332

AIMS Mathematics

2025, Volume 10, Issue 12: 30331-30353. doi: 10.3934/math.20251332

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Riemann solitons on perfect fluid within $ f ({r}, {T^{2}}) $-gravity

1.
Department of Mathematics, College of Science, Jazan University, P.O. Box 114, Jazan 45142, Kingdom of Saudi Arabia
2.
Department of pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran
3.
Department of Mathematics, Payame Noor University, P.O. Box 19395-4697, Tehran, Iran

Received: 10 October 2025 Revised: 06 December 2025 Accepted: 20 December 2025 Published: 24 December 2025
MSC : 53C21, 53C25, 53E20, 53Z05

This work is devoted to the study of Riemann solitons in the setting of the energy-momentum squared gravity framework, expressed as $ f(r, T^2) $, regarded as a deformation of Einstein's general relativity. Our attention is placed on the particular model $ f(r, T^2) = r+\lambda T^2 $, coupled with a perfect fluid, where the dynamics naturally admit Riemann solitons. Within the steady formulation of such solitons, we obtain the corresponding fluid relation of state under $ f(r, T^2) $-gravity. Moreover, by exploiting the solitonic structure, we further analyze the admissibility of energy conditions, the emergence of black hole geometries, and the manifestation of singularities in the presence of a perfect fluid for this modified gravitational scenario.
- $ f (r, T^2) $-gravity,
- conformal Ricci solitons,
- perfect fluid,
- concircular vector field,
- black holes,
- singularity
Citation: Wedad A Alharbi, Shahroud Azami, Mehdi Jafari, Abdul Haseeb. Riemann solitons on perfect fluid within $ f ({r}, {T^{2}}) $-gravity[J]. AIMS Mathematics, 2025, 10(12): 30331-30353. doi: 10.3934/math.20251332

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Abstract

This work is devoted to the study of Riemann solitons in the setting of the energy-momentum squared gravity framework, expressed as $ f(r, T^2) $, regarded as a deformation of Einstein's general relativity. Our attention is placed on the particular model $ f(r, T^2) = r+\lambda T^2 $, coupled with a perfect fluid, where the dynamics naturally admit Riemann solitons. Within the steady formulation of such solitons, we obtain the corresponding fluid relation of state under $ f(r, T^2) $-gravity. Moreover, by exploiting the solitonic structure, we further analyze the admissibility of energy conditions, the emergence of black hole geometries, and the manifestation of singularities in the presence of a perfect fluid for this modified gravitational scenario.

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