On mixed super quasi-Einstein manifolds with Ricci-Bourguignon solitons

Abstract: This paper delves into the study of mixed super quasi-Einstein manifolds of dimension $n$ (for short, ${\rm M<sup>{n}_{SQE}}$), focusing on their geometric and physical attributes. Initially, we explore several properties of ${\rm M<sup>{n}_{SQE}}$, including conformal Ricci pseudosymmetry, Einstein's field equation, and the space-matter tensor. Subsequently, we characterize mixed super quasi-Einstein manifolds that admit Ricci-Bourguignon solitons. We establish that if the generator vector field is torse-forming, the manifold reduces to a pseudo generalized quasi-Einstein manifold, and we provide a detailed characterization of the eigenvalue problem associated with the symmetric tensor. To substantiate our findings, we construct an example to illustrate the existence of mixed super quasi-Einstein spacetime.