$ h $-Almost conformal $ \eta $-Ricci–Bourguignon solitons on Bulk viscous fluid string spacetimes with anti-torqued vector fields

Awatif Al-Jedani; Sunil Kumar Yadav; Sameh Shenawy; Carlo Mantica; Awatif Al-Jedani; Sunil Kumar Yadav; Sameh Shenawy; Carlo Mantica

doi:10.3934/math.2026604

AIMS Mathematics

2026, Volume 11, Issue 5: 14715-14734. doi: 10.3934/math.2026604

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Research article

$ h $-Almost conformal $ \eta $-Ricci–Bourguignon solitons on Bulk viscous fluid string spacetimes with anti-torqued vector fields

1.
Department of Mathematics and Statistic, College of Science, University of Jeddah, Jeddah 23890, Saudi Arabia
2.
Department of Applied Science and Humanities, United College of Engineering & Research, UPSIDC, Industrial Area, Naini, Prayagraj, Uttar Predesh, India
3.
Basic Science Department, Modern Academy for Engineering and Technology, Maadi 4411602, Egypt
4.
Physics Department Aldo Pontremoli, Universita degli Studi di Milano and I.N.F.N. Sezione di Milano, Via Celoria 16, 20133 Milano, Italy

Received: 31 December 2025 Revised: 11 March 2026 Accepted: 17 April 2026 Published: 25 May 2026
MSC : 53B30, 53C25, 53C44, 53C50, 53C80

The present paper investigates the role of anti-torqued vector fields in bulk viscous fluid string (BVFS) space-times characterized by the total pressure $ \alpha $, energy density $ \rho $, and string tension $ \beta $, admitting an $ h $-almost conformal $ \eta $-Ricci-Bourguignon soliton ($ h $-ACERBS). The analysis is carried out within the framework of BVFS spacetimes incorporating bulk viscosity together with an anti-torqued vector field, where the underlying metric satisfies the $ h $-ACERBS condition. Particular emphasis is placed on the physical significance of the conformal pressure $ \bar{p} $ arising in the presence of such solitons and vector fields. Within this geometric and physical setting, the validity of the standard energy conditions is examined, along with criteria related to black-hole formation and the implications of Penrose's singularity theorem. In addition, generalized Liouville and Poisson equations associated with the $ h $-ACERBS structure are derived and analyzed. The harmonic properties of $ h $-ACERBS on BVFS space-times endowed with anti-torqued vector fields are also investigated, providing further insight into the interplay between the underlying geometric structures and their physical interpretations.
- Lorentzian spacetime manifold,
- Bulk viscous fluid string space-times,
- anti-torqued vector fields,
- Ricci–Bourguignon solitons
Citation: Awatif Al-Jedani, Sunil Kumar Yadav, Sameh Shenawy, Carlo Mantica. $ h $-Almost conformal $ \eta $-Ricci–Bourguignon solitons on Bulk viscous fluid string spacetimes with anti-torqued vector fields[J]. AIMS Mathematics, 2026, 11(5): 14715-14734. doi: 10.3934/math.2026604

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Abstract

The present paper investigates the role of anti-torqued vector fields in bulk viscous fluid string (BVFS) space-times characterized by the total pressure $ \alpha $, energy density $ \rho $, and string tension $ \beta $, admitting an $ h $-almost conformal $ \eta $-Ricci-Bourguignon soliton ($ h $-ACERBS). The analysis is carried out within the framework of BVFS spacetimes incorporating bulk viscosity together with an anti-torqued vector field, where the underlying metric satisfies the $ h $-ACERBS condition. Particular emphasis is placed on the physical significance of the conformal pressure $ \bar{p} $ arising in the presence of such solitons and vector fields. Within this geometric and physical setting, the validity of the standard energy conditions is examined, along with criteria related to black-hole formation and the implications of Penrose's singularity theorem. In addition, generalized Liouville and Poisson equations associated with the $ h $-ACERBS structure are derived and analyzed. The harmonic properties of $ h $-ACERBS on BVFS space-times endowed with anti-torqued vector fields are also investigated, providing further insight into the interplay between the underlying geometric structures and their physical interpretations.

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