Entanglement degradation in regular and singular spacetimes

TL;DR

This paper investigates how quantum entanglement degrades near various black hole horizons, comparing different spacetime geometries and revealing that entanglement behavior can distinguish between these backgrounds.

Contribution

It provides a detailed analysis of entanglement negativity in multiple regular and singular black hole spacetimes, introducing a Rindler approximation and examining extremal limits.

Findings

Reissner-Nordstr"om black holes show a local minimum in entanglement negativity.

Schwarzschild-de Sitter spacetime best preserves entanglement among studied geometries.

High-frequency modes are less affected by entanglement degradation.

Abstract

We study entanglement degradation near the horizons of regular, Reissner-Nordstr\"om, 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 $\rho$ 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 $a_0$. 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 $\omega$ and the acceleration $a_0$. 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-Nordstr\"om metric, for which $\mathcal{N}$ exhibits a shallow local minimum at a particular value of the charge. We also find that the Reissner-Nordstr\"om 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.