Conformal η-Ricci–Bourguignon soliton in general relativistic spacetime

Abstract

In this research paper, we determine the nature of conformal $\eta$-Ricci–Bourguignon soliton on a general relativistic spacetime with torse forming potential vector field. Besides this, we evaluate a specific situation of the soliton when the spacetime admitting semi-symmetric energy–momentum tensor with respect to conformal $\eta$-Ricci–Bourguignon soliton, whose potential vector field is torse-forming. Next, we explore some characteristics of curvature on a spacetime that admits conformal $\eta$-Ricci–Bourguignon soliton. In addition, we turn up some physical perception of dust fluid, dark fluid and radiation era in a general relativistic spacetime in terms of conformal $\eta$-Ricci–Bourguignon soliton. Finally, we examine necessary and sufficient conditions for a 1-form $\eta$, which is the $g$-dual of the vector field $\xi$ on general relativistic spacetime to be a solution of the Schrödinger–Ricci equation.