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# A simplified derivation of stimulated emission by black holes

(Impact Factor: 3.1). 12/1998; 4(4):L149. DOI: 10.1088/0264-9381/4/4/014

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.

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• "If that observer would send her own c modes into the black hole, the relative blue-shift 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 late-time blue-shifted " 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 (grey-body factor) whose parameters are implicit in the coefficients in Eq. (1). "
##### Article: Black holes as bosonic Gaussian channels
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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 one-mode bosonic Gaussian channels we find that (with one exception) the black hole Gaussian channels lie in the non-entanglement breaking subset of the lossy channels C(loss), amplifying channels C(amp) and classical-noise 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.
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• "Is there a model describing this kind of late-time 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 late-time massless scalar quantum field. "
##### Article: The capacity of black holes to transmit quantum information
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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 single-letter 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 non-vanishing, allowing for the perfect reconstruction of quantum information. We also find that the complementary channel (transmitting entanglement behind the horizon) is entanglement-breaking 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 non-vanishing 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 no-cloning theorem is upheld at the same time. The results furthermore imply that no quantum firewall exists, and sheds new light on black hole complementarity.
Journal of High Energy Physics 10/2013; 2014(5). DOI:10.1007/JHEP05(2014)095 · 6.22 Impact Factor
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• "The additional term γc k turns out to be necessary for a consistent treatment of black hole thermodynamics [9], and can be accounted for by using an effective Hamiltonian with an extra term (compared to Eq. 3) that describes scattering of late-time modes c k by the static black hole horizon, with an interaction strength g ′ : "
##### Article: Black holes conserve information in curved-space quantum field theory
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ABSTRACT: The fate of classical information incident on a quantum black hole has been the subject of an ongoing controversy in theoretical physics, because a calculation within the framework of semi-classical curved-space quantum field theory appears to show that the incident information is irretrievably lost, in contradiction to time-honored principles such as time-reversibility and unitarity. Here, we show within this framework embedded in quantum communication theory that signaling from past to future infinity in the presence of a Schwarzschild black hole can occur with arbitrary accuracy, and thus that classical information is not lost in black hole dynamics. The calculation relies on a treatment that is manifestly unitary from the outset, where probability conservation is guaranteed because black holes stimulate the emission of radiation in response to infalling matter. This stimulated radiation is non-thermal, and contains all of the information about the infalling matter, while Hawking radiation contains none of it.