Black hole perturbations in the modified generalized Chaplygin gas model

We study blackhole in the Modified Generalized Chaplygin Gas (MGCG) model, a modified gravity framework proposed to unify dark matter and dark energy. The resulting spacetime is asymptotically non-flat and feature two distinct horizons, determined by the Chaplygin parameter $α$. Observational constraints favor negative values of $α$, which restrict the allowed parameter space. Through linear perturbation analysis, we show that this blackhole remain stable under both scalar and electromagnetic perturbation. The corresponding quasinormal mode spectra depend sensitively on the MGCG parameters, indicating that this cosmological model leaves characteristic imprints on blackhole oscillations. These results suggest that gravitational-wave observations of blackhole ringdowns may provide a means of constraining MGCG and testing unified dark sector scenarios in the strong-field regime.