Constraining Redshift Parametrization Models with Recentmost Data : Impacts on an Accretion Disc around Finslerian Kiselev Black Hole

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 models. The logarithmic mass ratio $\log_{10}[M(z)/M_0]$ is found to be highly sensitive to the redshift-dependent evolution of $ω(z)$, 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. 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.

💡 Research Summary

The paper investigates how the mass of a black hole evolves when it is embedded in a cosmological background described by a Modified Chaplygin Gas (MCG) and subject to various dark‑energy (DE) equation‑of‑state (EoS) parametrizations. Four redshift‑dependent parametrizations are considered: Linear (ω(z)=ω₀+ω₁z), Logarithmic (ω(z)=ω₀+ω₁ ln(1+z)), CPL (Chevallier‑Polarski‑Linder, ω(z)=ω₀+ω₁ z/(1+z)), and JBP (Jassal‑Bagla‑Padmanabhan, ω(z)=ω₀+ω₁ z/(1+z)²). The authors first constrain the free parameters (ω₀, ω₁) of each model using the differential‑age (cosmic‑chronometer) measurements of the Hubble parameter H(z). A total of 39 H(z) data points spanning 0 ≤ z ≲ 2.5 are compiled from recent literature, and a standard χ² minimization yields best‑fit values. The Linear, Logarithmic and CPL parametrizations produce only mild evolution of ω(z), staying close to a constant negative value throughout the redshift range, whereas the JBP model exhibits a rapid transition to ω < ‑1 (phantom regime) at z ≈ 1.5–2.

Having fixed the background dynamics, the authors turn to the local strong‑gravity sector. They adopt a Finslerian version of the Kiselev black‑hole solution, which generalises the usual Schwarzschild–de Sitter metric by adding a term proportional to r^{‑3ω_s‑1} that encodes the surrounding fluid’s EoS parameter ω_s. The metric is further embedded in Rastall gravity, introducing a non‑conservation parameter λ that couples the Ricci scalar to the energy‑momentum tensor. The resulting lapse function reads f(r)=1‑2M/r‑c r^{‑3ω_s‑1}+Q²/r², where c is the Kiselev “quintessence” strength and Q the electric charge. The horizons (black‑hole and cosmological) and associated surface gravities are obtained analytically.

Mass accretion (or loss) is modelled using the Babichev‑et‑al. (2004) formalism for a perfect fluid with density ρ and pressure p: \dot M = 4π r_h² (ρ + p) v_r, where v_r is the radial inflow velocity evaluated at the black‑hole horizon r_h. The total fluid density and pressure are taken as the sum of the MCG component and the DE component defined by the chosen ω(z). Consequently, the sign of (ρ + p) is governed by ω(z): for ω > ‑1 (quintessence) the term is positive and the black hole gains mass, while for ω < ‑1 (phantom) it becomes negative and the black hole loses mass.

The authors integrate the accretion equation over redshift to obtain the logarithmic mass ratio log₁₀