Entanglement degradation in regular and singular spacetimes

We study entanglement degradation near the horizons of regular, Reissner-Nordström, and Schwarzschild-de Sitter black holes, considering the Bardeen, Hayward, and generalized Hayward metrics as regular black holes. To this end, we compute the entanglement negativity, mathcal{N}, for two Unruh-like modes of a scalar field shared by Alice, who is inertial, and Rob, who hovers at a fractional offset ρ outside the horizon of the backgrounds under consideration. For each geometry, we locally approximate the metric by a Rindler patch characterized by Rob's proper acceleration a₀. Because this Rindler approximation breaks down near the extremal limit, we also compute a near-extremal cutoff. Tracing over the inaccessible Rindler wedge yields a mixed Alice-Rob state, from which we evaluate mathcal{N} as a function of the mode frequency ω and the acceleration a₀. In all geometries considered, except for one, mathcal{N} increases monotonically with the parameter distinguishing that geometry form the Schwarzschild one. The exception is the Reissner-Nordström metric, for which mathcal{N} exhibits a shallow local minimum at a particular value of the charge. We also find that the Reissner-Nordström metric is the only background for which the negativity falls below that of the Schwarzschild case. Among all cases studied, the Schwarzschild-de Sitter spacetime provides the strongest protection of entanglement. Finally, across all backgrounds, high-frequency modes undergo less degradation than low-frequency modes. These results suggest that entanglement may serve as a useful probe for distinguishing Schwarzschild spacetime from other geometries.