Article
A simplified derivation of stimulated emission by black holes
Classical and Quantum Gravity (Impact Factor: 3.17). 12/1998; 4(4):L149. DOI: 10.1088/02649381/4/4/014
ABSTRACT
A black hole, when acting as a scatterer for quanta in a single mode of a massless scalar field, is known to convert any ingoing Gibbs state of that mode into an outgoing Gibbs state (with some other mean particle number). The author presents a simple derivation for this property, which may help to clarify what relation, if any, it bears to the microscopic structure of the black hole horizon.

 "This stimulated emission makes the radiation nonthermal and thus capable of storing information. There have been studies (see e.g.,[9] [10] [11] [12] [13] [14] [15] [16]) regarding information content of corrected spectrum, form the point of view of information theory (von Neumann entropy, channel capacity, etc.). In this work, without committing to any particular notion of information content or without making an attempt to restore unitarity by a process, we will discuss the possibility of reconstruction of the initial state of the field from the resultant radiation in a collapse process. "
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ABSTRACT: The crux of the black hole information paradox is related to the fact that the complete information about the initial state of a quantum field in a collapsing spacetime is not available to future asymptotic observers, belying the expectations from a unitary quantum theory. We study the imprints of the initial quantum state, contained in the distortions of the black hole radiation from the thermal spectrum, which can be detected by the asymptotic observers. We identify the class of instates which can be fully reconstructed from the information contained in the distortions at the semiclassical level. Even for the general instate, we can uncover a specific amount of information about the initial state. For a large class of initial states, some specific observables defined in the initial Hilbert space are completely determined from the resulting final spectrum. These results suggest that a \textit{classical} collapse scenario ignores this richness of information in the resulting spectrum and a consistent quantum treatment of the entire collapse process might allow us to retrieve all the information from the spectrum of the final radiation. 
 "If that observer would send her own c modes into the black hole, the relative blueshift of these modes with respect to the black hole horizon modes implies that the support of the quantum fields associated with c modes is disjoint from that of the a and b modes. As a consequence, the outgoing field operator A should resolve into a superposition not just of the ingoing horizon modes a and b, but also the ingoing latetime blueshifted " signal " modes c [8]. Using the expanded Bogoliubov transformation (1) Sorkin showed that the resulting expression for the radiation experienced by a stationary observer suspended far away from the black hole horizon precisely reproduces the standard Hawking radiation effect including the effect of a black hole potential (greybody factor) whose parameters are implicit in the coefficients in Eq. (1). "
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ABSTRACT: We identify the quantum channels corresponding to the interaction of a Gaussian quantum state with an already formed Schwarzschild black hole. Using recent advances in the classification of onemode bosonic Gaussian channels we find that (with one exception) the black hole Gaussian channels lie in the nonentanglement breaking subset of the lossy channels C(loss), amplifying channels C(amp) and classicalnoise channels B_2. We show that the channel parameters depend on the black hole mass and the properties of the potential barrier surrounding it. This classification enables us to calculate the classical and quantum capacity of the black hole and to estimate the quantum capacity where no tractable quantum capacity expression exists today. We discuss these findings in the light of the black hole quantum information loss problem. 
 "Is there a model describing this kind of latetime interaction between quantum information and an already formed black hole? Indeed, this situation has been treated before [27] (see [16] for further analysis). Sorkin describes an interaction between a black hole formed by a gravitational collapse and a latetime massless scalar quantum field. "
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ABSTRACT: We study the properties of the quantum information transmission channel that emerges from the quantum dynamics of particles interacting with a black hole horizon. We calculate the quantum channel capacity in two limiting cases where a singleletter capacity is known to exist: the limit of perfectly reflecting and perfectly absorbing black holes. We find that the perfectly reflecting black hole channel is closely related to the Unruh channel and that its capacity is nonvanishing, allowing for the perfect reconstruction of quantum information. We also find that the complementary channel (transmitting entanglement behind the horizon) is entanglementbreaking in this case, with vanishing capacity. We calculate the quantum capacity of the black hole channel in the limit of a perfectly absorbing black hole and find that this capacity vanishes, while the capacity of the complementary channel is nonvanishing instead, implying that the quantum state itself survives unharmed beyond the horizon. These results together imply that the equivalence theorem holds for black holes, while the quantum nocloning theorem is upheld at the same time. The results furthermore imply that no quantum firewall exists, and sheds new light on black hole complementarity.
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