Dark Energy Contaminated Black Hole Solution: A Drive Through the Thermodynamic Properties

Abstract: We investigate the evolution of black hole mass within a cosmological background modeled by a Modified Chaplygin Gas (MCG) under various dark energy equation of state parametrizations, including Linear, Logarithmic, CPL, JBP, FSLL-II, and Barboza--Alcaniz (BA) models. The logarithmic mass ratio $\log_{10}[M(z)/M_0]$ is found to be highly sensitive to the redshift-dependent evolution of $\omega(z)$, with gentle slopes in Linear, Logarithmic, and CPL models indicating quasi-static accretion, steep slopes in JBP corresponding to rapid late-time variations, and non-monotonic behaviour in FSLL-II and BA highlighting transient suppression or enhancement of accretion due to repulsive dark energy effects. Peaks, minima, and amplitude offsets in the mass ratio reflect the dynamic interplay between horizon thermodynamics, the evolving pressure of the MCG, and cosmic expansion, illustrating how the black hole mass growth is directly influenced by both the temporal evolution of dark energy and the effective gravitational potential 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.