Entanglement degradation in regular and singular spacetimes

Abstract

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 $a_0$. 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 $ω$ 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-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.

Figures (6)

• Figure 1: Penrose (conformal) diagram of Minkowski spacetime showing a uniformly accelerated (Rindler) observer $R$ and an inertial observer $A$. The null lines $x=\pm t$ partition spacetime into four connected regions (Rindler wedges). For observers with constant proper acceleration in the right wedge ($x>|t|$), these null boundaries are acceleration (Rindler) horizons: the future horizon $\mathcal{H}^+$ is $t=x$ and the past horizon $\mathcal{H}^-$ is $t=-x$. The worldline of $R$ lies completely within the right (first) Rindler wedge and is asymptotic to $\mathcal{H}^\pm$.
• Figure 2: Negativity as a function of the charge-to-mass ratio $Q/M$ for several frequencies $\omega$ at fixed $\rho$. A minimum in the negativity is present at $Q/M\approx0.879$.
• Figure 3: Negativity in the RN case, normalized to the corresponding Schwarzschild value at $Q/M=0$.
• Figure 4: Negativity as a function of the magnetic charge $g$ for selected frequencies $\omega$.
• Figure 5: Negativity as a function of the length parameter $\ell$, for various mode frequencies $\omega$.