$h$-Almost conformal $\eta$-Ricci–Bourguignon solitons on Bulk viscous fluid string spacetimes with anti-torqued vector fields

The present paper investigates the role of anti-torqued vector fields in bulk viscous fluid string (BVFS) space-times characterized by the total pressure $\alpha$, energy density $\rho$, and string tension $\beta$, admitting an $h$-almost conformal $\eta$-Ricci-Bourguignon soliton ( $h$-ACERBS). The analysis is carried out within the framework of BVFS spacetimes incorporating bulk viscosity together with an anti-torqued vector field, where the underlying metric satisfies the $h$-ACERBS condition. Particular emphasis is placed on the physical significance of the conformal pressure $\overline{p}$ arising in the presence of such solitons and vector fields. Within this geometric and physical setting, the validity of the standard energy conditions is examined, along with criteria related to black-hole formation and the implications of Penrose's singularity theorem. In addition, generalized Liouville and Poisson equations associated with the $h$-ACERBS structure are derived and analyzed. The harmonic properties of $h$-ACERBS on BVFS space-times endowed with anti-torqued vector fields are also investigated, providing further insight into the interplay between the underlying geometric structures and their physical interpretations.