Accretion Induced Mass Evolution of a Schwarzschild Black Hole Under BRB Redshift Parameterized Dark Energy: A Differential Ages Constraint Analysis

The Schwarzschild black hole (BH) constitutes a fundamental exact solution of Einstein’s field equations in general relativity, representing the exterior geometry of a spherically symmetric mass in a vacuum in the absence of a cosmological constant Λ. However, the accelerated expansion of the universe is attributed to dark energy (DE) which is intrinsically linked to a non-zero cosmological constant Λ. Hence, incorporating DE naturally requires the Λ-modified Einstein field equations. To investigate late-time cosmic acceleration, the Biswas Roy Biswas (BRB) parameterization of the dark-energy equation of state has been adopted. This model emphasizes low-redshift dynamics and offers significant flexibility in constraining observational data from SNeIa, BAO and CMB. Using a dataset of eighty five differential age measurements, we obtain the corresponding confidence contours and marginalized distributions for the free parameters. Spherical accretion of BRB type DE onto a Schwarzschild BH within the framework is studied which has been established by Bondi and Michel. Bondi’s analysis shows that stationary, spherically symmetric flow becomes critical at the sonic point, where the infall velocity equals the local sound speed. In our formulation, the fluid equations similarly exhibit a singular structure at the sonic point, and only particular transonic solutions remain physically admissible. These solutions determine the Bondi accretion rate for BRB type DE onto the Schwarzschild spacetime. Our results indicate that, over the redshift interval 0 to 3, a Schwarzschild BH could gain approximately 55.331% of its present mass due to the accretion of BRB type DE.