The paper’s main goal is to investigate the impact of h-almost conformal \(\eta\) -Ricci-Bourguignon soliton in Bianchi type-I space-time coupled with bulk viscosity and magnetic field in Rosen’s bimetric theory of gravitation. Additionally, we demonstrate that some specific physical properties of a Bianchi type-I space-time that permit the inclusion of bulk viscosity and magnetic field in Rosen’s bimetric theory with a conformal vector field, where the metric satisfies h-almost conformal \(\eta\) -Ricci-Bourguignon soliton. Moreover, we illustrate some physical relevance of conformal pressure \(\widetilde{p}\) in terms of h-almost conformal \(\eta\) -Ricci-Bourguignon soliton in Rosen’s bimetric theory. Within this ongoing work, using such solitons, we analyze the various energy conditions, some black holes criteria, and Penrose’s singularity theorem in Bianchi type-I space-time coupled with bulk viscosity and magnetic field in Rosen’s bimetric theory of gravitation. We further investigate the generalized Liouville and Poisson equations associated with the h-almost conformal \(\eta\) -Ricci-Bourguignon soliton on a Bianchi type-I space-time. Finally, in the context of Rosen’s bimetric theory attached with bulk viscosity and magnetic field, we explore the harmonic aspects of h-almost conformal \(\eta\) -Ricci-Bourguignon soliton on such a space-time.
