We are not particles falling into a black hole, we are one wave, falling forever, and the light we see in the sky is only the interference of our own footsteps.
In this paper we extend the investigation of Adami and Ver Steeg [Class. Quantum Grav. \textbf{31}, 075015 (2014)] to treat the process of black hole particle emission effectively as the analogous quantum optical process of parametric down conversion (PDC) with a dynamical (depleted vs. non-depleted) `pump' source mode which models the evaporating black hole (BH) energy degree of freedom. We investigate both the short time (non-depleted pump) and long time (depleted pump) regimes of the quantum state and its impact on the Holevo channel capacity for communicating information from the far past to the far future in the presence of Hawking radiation. The new feature introduced in this work is the coupling of the emitted Hawking radiation modes through the common black hole `source pump' mode which phenomenologically represents a quantized energy degree of freedom of the gravitational field. This (zero-dimensional) model serves as a simplified arena to explore BH particle production/evaporation and back-action effects under an explicitly unitary evolution which enforces quantized energy/particle conservation. Within our analogous quantum optical model we examine the entanglement between two emitted particle/anti-particle and anti-particle/particle pairs coupled via the black hole (BH) evaporating `pump' source. We also analytically and dynamically verify the `Page information time' for our model which refers to the conventionally held belief that the information in the BH radiation becomes significant after the black hole has evaporated half its initial energy into the outgoing radiation. Lastly, we investigate the effect of BH particle production/evaporation on two modes in the exterior region of the BH event horizon that are initially maximally entangled, when one mode falls inward and interacts with the black hole, and the other remains forever outside and non-interacting.
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.
Presentations of black hole complementarity by van Dongen and de Haro, as well as by 't Hooft, suffer from a mistaken claim that interactions between matter falling into a black hole and the emitted Hawking-like radiation should lead to a failure of commutativity between space-like-related observables localized inside and outside the black hole. I show that this conclusion is not supported by our standard understanding of quantum interactions. We have no reason to believe that near-horizon interactions will threaten microcausality. If these interactions reliably transfer information to the outgoing radiation, then this response to Hawking's information loss argument should amount to a version of the bleaching scenario. I argue that the challenge facing black hole complementarity is that of reconciling this commitment to bleaching with the expectation that the event horizon will be locally unremarkable. This challenge is most promisingly met by proposals that postulate a consistent account of the limitations of our local semi-classical theories, but no support is added to these postulates by appeals to verificationism or to the interactions considered by 't Hooft.