Entanglement and correlations near extremality: CFTs dual to Reissner-Nordström AdS5

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.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.

gr-qcCross-listedarXiv:2603.21857Mar 24, 2026

Tomás Andrade, Sebastian Fischetti, Donald M. Marolf +2 more

We use the AdS/CFT correspondence to study models of entanglement and correlations between two d = 4 CFTs in thermofield double states at finite chemical potential. Our bulk spacetimes are planar Reissner-Nordström AdS black holes. We compute both thermo-mutual information and the two-point correlators of large-dimension scalar operators, focussing on the small-temperature behavior — an infrared limit with behavior similar to that seen at large times. The interesting feature of this model is of course that the entropy density remains finite as T → 0 while the bulk geometry develops an infinite throat. This leads to a logarithmic divergence in the scale required for non-zero mutual information between equal-sized strips in the two CFTs, though the mutual information between one entire CFT and a finite-sized strip in the other can remain non-zero even at T =0. Furthermore,despitetheinfinitethroat,therecanbeextremallychargedoperators for which the two-point correlations remain finite as T → 0. This suggests an interestingly mixed picture in which some aspects of the entanglement remain localized on scales set by the chemical potential, while others shift to larger and larger scales. We also comment on implications for the localized-quasiparticle picture of entanglement.We use the AdS/CFT correspondence to study models of entanglement and correlations between two d = 4 CFTs in thermofield double states at finite chemical potential. Our bulk spacetimes are planar Reissner-Nordström AdS black holes. We compute both thermo-mutual information and the two-point correlators of large-dimension scalar operators, focussing on the small-temperature behavior — an infrared limit with behavior similar to that seen at large times. The interesting feature of this model is of course that the entropy density remains finite as T → 0 while the bulk geometry develops an infinite throat. This leads to a logarithmic divergence in the scale required for non-zero mutual information between equal-sized strips in the two CFTs, though the mutual information between one entire CFT and a finite-sized strip in the other can remain non-zero even at T =0. Furthermore,despitetheinfinitethroat,therecanbeextremallychargedoperators for which the two-point correlations remain finite as T → 0. This suggests an interestingly mixed picture in which some aspects of the entanglement remain localized on scales set by the chemical potential, while others shift to larger and larger scales. We also comment on implications for the localized-quasiparticle picture of entanglement.

arXiv:1312.2839Journal of High Energy PhysicsApr 1, 201424 citations

Quantum Correlations Beyond Entanglement

Alexander Streltsov

SpringerBriefs in physicsNov 1, 201417 citations

Characterizing Entanglement and Quantum Correlations Constrained by Symmetry

Jordi Tura i Brugués

Springer thesesDec 3, 201613 citations

Complex scaling approach to quasinormal modes of Schwarzschild and Reissner--Nordström black holes

Shoya Ogawa, Takuya Hirose, Okuto Morikawa

We study black-hole quasinormal modes by applying the complex scaling method (CSM) to the perturbation equations of Schwarzschild and Reissner--Nordström black holes. The method converts the outgoing-wave boundary condition into a non-Hermitian eigenvalue problem, allowing quasinormal-mode frequencies to be computed within a common spectral framework. We first benchmark the method for the Schwarzschild Regge--Wheeler equation and then extend it to the Reissner--Nordström family, including the extremal limit. Our results show that CSM provides a unified and flexible approach to the computation of black-hole quasinormal frequencies.We study black-hole quasinormal modes by applying the complex scaling method (CSM) to the perturbation equations of Schwarzschild and Reissner--Nordström black holes. The method converts the outgoing-wave boundary condition into a non-Hermitian eigenvalue problem, allowing quasinormal-mode frequencies to be computed within a common spectral framework. We first benchmark the method for the Schwarzschild Regge--Wheeler equation and then extend it to the Reissner--Nordström family, including the extremal limit. Our results show that CSM provides a unified and flexible approach to the computation of black-hole quasinormal frequencies.

hep-thCross-listedarXiv:2604.20442Apr 23, 2026

\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.