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arXiv:2504.00083 · Journal of High Energy Physics

Harvesting information across the horizon

Sijia Wang, María Rosa Preciado-Rivas, Robert B. Mann

Published Jul 25, 2025• 10 citations
arXivHTMLPDF

Abstract

A bstract The effect of black holes on entanglement harvesting has been of considerable interest over the past decade. Research involving stationary Unruh-DeWitt (UDW) detectors near a (2+1)-dimensional Bañados-Teitelboim-Zanelli (BTZ) black hole has uncovered phenomena such as entanglement shadows, entanglement amplification through black hole rotation, and differences between bipartite and tripartite entanglement. For a (1+1)-dimensional Schwarzschild black hole, it has been shown that two infalling UDW detectors can harvest entanglement from the scalar quantum vacuum even when separated by an event horizon. In this paper, we calculate the mutual information between two UDW detectors coupled to a massless quantum scalar field, with the detectors starting at rest and falling radially into a non-rotating (2+1)-dimensional BTZ black hole. The trajectory of the detectors includes regions where both detectors are switched on outside of the horizon; where one detector is switched on inside of the horizon while the other switches on outside; and where both detectors switch on inside of the horizon. We investigate different black hole masses, detector energy gaps, widths and temporal separations of the detector switching functions, and field boundary conditions. We find that black holes — even the simplest kind having constant curvature — significantly affect the correlation properties of quantum fields in the vacuum state. These correlations, both outside and inside the horizon, can be mapped out by infalling detectors.

DOI
10.1007/jhep07(2025)254

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A bstract The effect of black holes on entanglement harvesting has been of considerable interest over the past decade. Research involving stationary Unruh-DeWitt (UDW) detectors near a (2+1)-dimensional Bañados-Teitelboim-Zanelli (BTZ) black hole has uncovered phenomena such as entanglement shadows, entanglement amplification through black hole rotation, and differences between bipartite and tripartite entanglement. For a (1+1)-dimensional Schwarzschild black hole, it has been shown that two infalling UDW detectors can harvest entanglement from the scalar quantum vacuum even when separated by an event horizon. In this paper, we calculate the mutual information between two UDW detectors coupled to a massless quantum scalar field, with the detectors starting at rest and falling radially into a non-rotating (2+1)-dimensional BTZ black hole. The trajectory of the detectors includes regions where both detectors are switched on outside of the horizon; where one detector is switched on inside of the horizon while the other switches on outside; and where both detectors switch on inside of the horizon. We investigate different black hole masses, detector energy gaps, widths and temporal separations of the detector switching functions, and field boundary conditions. We find that black holes — even the simplest kind having constant curvature — significantly affect the correlation properties of quantum fields in the vacuum state. These correlations, both outside and inside the horizon, can be mapped out by infalling detectors.
One consequence of the cosmic censorship conjecture is that any topological structure will ultimately collapse to within the horizons of a set of black holes, and as a result, an external classical observer will be unable to probe it. However, a single two-level quantum system [Unruh–DeWitt (UDW) detector] that remains outside of the horizon has been shown to distinguish between a black hole and its associated geon counterpart via its different response rates. Here, we extend this investigation of the quantum vacuum outside of an ℝP2 geon by considering the entanglement structure of the vacuum state of a quantum scalar field in this spacetime, and how this differs from its Banados–Teitelboim–Zanelli (BTZ) black hole counterpart. Employing the entanglement harvesting protocol, where field entanglement is swapped to a pair of UDW detectors, we find that the classically hidden topology of the geon can have an appreciable difference in the amount of entanglement harvested in the two spacetimes for sufficiently small mass. In this regime, we find that detectors with a small energy gap harvest more entanglement in the BTZ spacetime; however, as the energy gap increases, the detectors harvest more entanglement in a geon spacetime. The energy gap at the crossover is dependent on the black hole mass, occurring at lower values for lower masses. This also impacts the size of the entanglement shadow, the region near the horizon where the detectors cannot harvest entanglement. Small gap detectors experience a larger entanglement shadow in a geon spacetime, whereas for large gap detectors, the shadow is larger in a BTZ spacetime.
We carry out the first investigation of the entanglement and mutual information harvesting protocols for detectors freely falling into a black hole. Working in (1+11+11+1)-dimensional Schwarzschild black hole spacetime, we consider two pointlike Unruh-DeWitt detectors in different combinations of free-falling and static trajectories. Employing a generalization of relative velocity suitable for curved spacetimes, we find that the amount of correlations extracted from the black hole vacuum, at least outside the near-horizon regime, is largely kinematic in origin (i.e., it is mostly due to the relative velocities of the detectors). Second, correlations can be harvested purely from the black hole vacuum even when the detectors are causally disconnected by the event horizon. Finally, we show that the previously known `entanglement shadow' near the horizon is indeed absent for the case of two free-falling-detectors, since their relative gravitational redshift remains finite as the horizon is crossed, in accordance with the equivalence principle.
We investigate the correlation harvesting protocol for mutual information between two Unruh-DeWitt detectors in a static Ba\~nados-Teitelboim-Zanelli black hole spacetime. Here, the effects coming from communication and change in proper separation of the detectors are set to be negligible so that only a black hole affects the extracted mutual information. We find that, unlike the entanglement harvesting scenario, harvested mutual information is zero only when a detector reaches an event horizon, and that although the Hawking effect and gravitational redshift both affect the extraction of mutual information, it is extreme Hawking radiation that inhibits the detectors from harvesting.
Abstract We implement the entanglement harvesting protocol, in which two Unruh–DeWitt detectors become entangled through local interactions with a quantum field, for the first time in the vicinity of a black hole. Our study, focusing on the BTZ black hole, reveals that black holes inhibit entanglement harvesting. For two detectors with fixed proper separation along the radial direction, we demonstrate that the entanglement harvested rapidly falls to zero as the detectors move closer to the horizon. This effect is a combination of black hole radiation and gravitational redshift, both generic properties of horizons, suggesting it is a general result for black holes.
Abstract The quantum vacuum has long been known to be characterized by field correlations between spacetime points. We show that such correlations—vacuum entanglement—in the environment of near-extremal black holes is significantly amplified (up to ten-fold) relative to their slowly rotating counterparts. We demonstrate this effect for rotating Banados–Teitelboim–Zanelli black holes by measuring the entanglement through the concurrence extracted from the vacuum via two-level quantum systems (Unruh–DeWitt detectors). The effect is manifest at intermediate distances from the horizon, and is most pronounced for near-extremal small mass black holes. The effect is also robust, holding for all boundary conditions of the field and at large spacelike detector separations. Smaller amplification occurs near the horizon, where we find that the entanglement shadow—a region near the black hole from which entanglement cannot be extracted—is diminished in size as the black hole’s angular momentum increases.
We explore entanglement harvesting using two Unruh-DeWitt (UDW) detectors linearly coupled to the scalar density of a massless spin-1/21/21/2 field in 1+11+11+1 Schwarzschild spacetime. We consider different vacua, including the Boulware, Hartle-Hawking-Israel (HHI), and Unruh vacua, and investigate various configurations of detector trajectories. We find that the transition rate of the static UDW detector exhibits the expected Planckian behavior in the HHI state, while the Unruh state leads to the Helmholtz free energy density of a fermionic thermal bath. We demonstrate that the near-horizon entanglement properties for static detectors in the HHI state have similar behavior to those in Minkowski vacua for uniformly accelerated detectors in Rindler spacetime. We further consider a different interaction Hamiltonian which breaks local Lorentz symmetry and find that the transition rate of the static detector still exhibits Planckian behavior in the HHI state, while in the Unruh state, it leads to the Helmholtz free energy density of a bosonic or fermionic thermal bath corresponding to the static or conformal 2-bein in interaction, respectively. We observe that the anti-Hawking effect enhances the entanglement between the two detectors while the gravitational redshift and Hawking radiation decrease it. In particular, due to the presence of the anti-Hawking effect, the mutual information and concurrence near the event horizon can be non-zero even for static detectors with static 2-bein, which is in contrast with the case of the scalar field. Conclusions are discussed.