Riemann solitons on spacetimes with pure radiation metrics

Rawan Bossly; Shahroud Azami; Dhriti Sundar Patra; Abdul Haseeb; Rawan Bossly; Shahroud Azami; Dhriti Sundar Patra; Abdul Haseeb

doi:10.3934/math.2025806

AIMS Mathematics

2025, Volume 10, Issue 8: 18094-18107. doi: 10.3934/math.2025806

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Riemann solitons on spacetimes with pure radiation metrics

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, Indian Institute of Technology Hyderabad, Sangareddy, Telangana, 502285, India

Received: 11 April 2025 Revised: 24 July 2025 Accepted: 28 July 2025 Published: 11 August 2025
MSC : 53C21, 53C44, 53E20

We investigate Riemann solitons within spacetimes characterized by pure radiation metrics that are conformally related to a vacuum spacetime. Additionally, it is shown that the Riemann solitons on spacetimes with pure radiation metrics are gradient Riemann solitons with a certain potential function. Moreover, we classify the potential vector fields of Riemann solitons as Ricci collineation, Killing, and Ricci bi-conformal.
- pure radiation metrics,
- Riemann soliton,
- Ricci collineation
Citation: Rawan Bossly, Shahroud Azami, Dhriti Sundar Patra, Abdul Haseeb. Riemann solitons on spacetimes with pure radiation metrics[J]. AIMS Mathematics, 2025, 10(8): 18094-18107. doi: 10.3934/math.2025806

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Abstract

We investigate Riemann solitons within spacetimes characterized by pure radiation metrics that are conformally related to a vacuum spacetime. Additionally, it is shown that the Riemann solitons on spacetimes with pure radiation metrics are gradient Riemann solitons with a certain potential function. Moreover, we classify the potential vector fields of Riemann solitons as Ricci collineation, Killing, and Ricci bi-conformal.

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