Constraining Redshift Parametrization Dark Energy Models with Recent-most Data : Impacts on an Accretion Disc around Finslerian Kiselev Black Hole

We investigate the evolution of black hole mass for a Finslerian Kiselev black hole embedded in a cosmological background under various dark energy equation of state parametrizations, including Linear, Chevallier-Polarski-Linder(CPL), Jassal-Bagla-Padmanabhan (JBP) and Logarithmic models. The logarithmic mass ratio [Formula: see text] is found to be highly sensitive to the redshift dependent evolution of the dynamical dark energy equation of state parameter [Formula: see text], with gentle slopes in Linear, Logarithmic and CPL models indicating quasi static accretion and steep slopes in JBP corresponding to rapid late time variations highlighting transient suppression or enhancement of accretion due to repulsive dark energy effects. The peaks, minima and amplitude variations in the mass ratio arise from the combined effects of horizon thermodynamics, the changing pressure of the quintessence like fluid and cosmic expansion. These features show that the mass evolution of the Finslerian Kiselev black hole is governed by dark energy dynamics and the effective gravitational influence of the surrounding cosmic fluid. Our results demonstrate that black hole accretion acts as a sensitive probe of the time dependent cosmic pressure landscape and provides physical insights into the coupling between local strong gravity and global accelerated expansion.