Solitonic geometry of Magneto fluid spacetimes: Ricci Bourguignon insights and energy momentum characterizations

Abstract

The main objective of our current article is to inspect the solitonic aspect of relativistic magneto-fluid spacetime if its metric is Ricci Bourguignon soliton. We explored some geometrical behaviour of magneto-fluid spacetime emerged with a Ricci Bourguignon soliton. We accomplished a few characterizations of magneto-fluid spacetime in relation to a Ricci bourguignon soliton with a $\varphi \left(Q\right)$-vector field, torse-forming vector field and conformal Killing vector field. Also, we determine the con-harmonically flat, $W_2$-flat and $Q_1$-flat curvature state of a magneto-fluid spacetime admitting Ricci bourguignon soliton. Eventually, we explored the magneto-fluid spacetime model characterized by a specific form of energy-momentum tensor in which the pressure equals the energy density. Also, we explicit an example to verify our result. Furthermore, this investigation may offer new insights into the magneto-geometric behaviour of compact astrophysical objects such as neutron stars and magnetars, and opens unexplored avenues for geometric modelling in magnetohydrodynamic engineering and modified gravity theories.