ABSTRACT This paper examines the impact of an almost Ricci‐Bourguignon soliton structure on the base and fiber manifolds of twisted warped product manifolds. We establish necessary and sufficient conditions for the existence of such solitons, providing a foundational framework for their analysis. Specifically, we explore the conditions under which an almost Ricci‐Bourguignon soliton transforms a twisted warped product manifold into an Einstein manifold. Additionally, we analyze the behavior of these solitons in twisted warped product manifolds that admit a conformal vector field, offering new insights into their geometric properties. The study is further extended to twisted warped product spacetimes, revealing novel perspectives on their curvature and soliton structures. Our results include the classification of almost Ricci‐Bourguignon solitons on twisted warped product manifolds, the characterization of Einstein manifolds within this framework, and the implications of conformal vector fields on the soliton structure. These findings significantly advance the understanding of almost Ricci‐Bourguignon solitons in the context of twisted warped product manifolds and their applications in differential geometry and theoretical physics. The paper also provides detailed proofs and conditions under which the base and fiber manifolds inherit the soliton structure, contributing to the broader study of geometric flows and their solutions.
Elsharkawy et al. (2025) studied this question.