Blackhole perturbations in the Modified Generalized Chaplygin Gas model

Abstract

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.

Figures (14)

• Figure 1: Parameter space showing allowed region under the MGCG blackhole horizon condition (light-shaded). The dark blue region, bounded by a closed thick black line (three straight edges and one curved), satisfies additional cosmological constraints. The curved boundary region corresponds to the near-extremal regime.
• Figure 2: Effective potentials ($V_\text{eff}$) for scalar perturbations as functions of radial distance $u$. Each panel corresponds to a different value of the MGCG parameter $\alpha$ (increasing from left to right), with $\Omega_m = 0.95$ fixed. Colored curves represent different multipole numbers $l$. The leftmost plot corresponds to the near-extremal black hole configuration.
• Figure 3: Variation of the real part of the QNM frequency with the MGCG parameter $\alpha$ for scalar field perturbations. The plot shows results for the fundamental mode with multipole number $l = 2$. Different colored curves correspond to different values of the cosmological parameter $\Omega_m$.
• Figure 4: Effective potentials ($V_\text{eff}$) for electromagnetic perturbations as functions of radial distance $u$. Plots are shown for different multipole numbers $l$, with the MGCG parameter fixed at $\alpha = -0.85$ and varying values of $\Omega_m$. The colored curves illustrate how the potential structure depends on $l$
• Figure 5: Imaginary part of the QNM frequency for scalar field perturbations as a function of the MGCG parameter $\alpha$. The plot corresponds to the fundamental mode with $l = 2$, with different colored curves representing various values of the cosmological parameter $\Omega_m$.