Causal Structure of Black Holes Immersed in a Chaplygin-like Dark Fluid Environment: Horizons and Singularities

In the present work, we study the causal structure of spherically symmetric black holes immersed in a Chaplygin-like dark fluid, emphasizing the impact of the fluid parameters on curvature and horizon formation. We show that the spacetime curvature is significantly stronger than in its similar counterpart, the Reissner–Nordström–de Sitter geometry with the same mass and charge, leading to modifications of the internal causal structure. For the presence of horizons, the Chaplygin black hole possesses an upper bound $Q\approx 0.556219M$, which is much smaller than that for Reissner–Nordström spacetime $Q_{critical}=M$ or for the Reissner–Nordström–de Sitter case $Q_{critical}=3M/2\sqrt{2}$, indicating that the black holes immersed in a Chaplygin-like dark fluid reach the extremal regime more easily. We derive a second critical condition for the Chaplygin cosmological parameter B, $B_c{Q}_c=4/3^9$, setting an upper bound on B for a multi-horizon solution.