Abstract This work analytically investigates the back-reaction of accreting matter onto a modified Schwarzschild black hole within a perturbative framework, assuming quasi-steady accretion. To address different physical scenarios, three accretion models dust, radiative and perfect fluid are examined, and systematic corrections to the metric coefficients are derived. From these corrections, explicit forms of the mass function are obtained, from which the corrected apparent horizon is determined. The thermodynamic properties of the system are also explored in light of these modifications. Our results show that, independent of the chosen energy-momentum tensor, the near-horizon behavior of the corrected geometry consistently reduces to the Vaidya form. This establishes the universality of the perturbative method in the context of modified Schwarzschild black holes and provides new insights into the interplay between accretion dynamics, horizon structure, and BH thermodynamics. We also compare the results for the Schwarzschild black hole, the perturbed Schwarzschild black hole, and the modified Schwarzschild black hole, and find that the modified Schwarzschild black hole exhibits stronger back-reaction effects than the others.
Bibi et al. (Mon,) studied this question.