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Register a new userThe Page curve of Hawking radiation from semiclassical geometry
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We consider a gravity theory coupled to matter, where the matter has a higher-dimensional holographic dual. In such a theory, finding quantum extremal surfaces becomes equivalent to finding the RT/HRT surfaces in the higher-dimensional theory. Using this we compute the entropy of Hawking radiation and argue that it follows the Page curve, as suggested by recent computations of the entropy and entanglement wedges for old black holes. The higher-dimensional geometry connects the radiation to the black hole interior in the spirit of ER=EPR. The black hole interior then becomes part of the entanglement wedge of the radiation. Inspired by this, we propose a new rule for computing the entropy of quantum systems entangled with gravitational systems which involves searching for islands in determining the entanglement wedge.
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We give a detailed treatment of the back-reaction effects on the Hawking spectrum in the semiclassical approach to the Hawking radiation. We solve the exact system of non linear equations giving the action of the system, by a rigorously convergent iterative procedure. The first two terms of such an expansion give the O(omega/M) correction to the Hawking spectrum.
Asymptotic Causal Diamonds (ACDs) are a natural flat space analogue of AdS causal wedges, and it has been argued previously that they may be useful for understanding bulk locality in flat space holography. In this paper, we use ACD-inspired ideas to argue that there exist natural candidates for Quantum Extremal Surfaces (QES) and entanglement wedges in flat space, anchored to the conformal boundary. When there is a holographic screen at finite radius, we can also associate entanglement wedges and entropies to screen sub-regions, with the system naturally coupled to a sink. The screen and the boundary provide two complementary ways of formulating the information paradox. We explain how they are related and show that in both formulations, the flat space entanglement wedge undergoes a phase transition at the Page time in the background of an evaporating Schwarzschild black hole. Our results closely parallel recent observations in AdS, and reproduce the Page curve. That there is a variation of the argument that can be phrased directly in flat space without reliance on AdS, is a strong indication that entanglement wedge phase transitions may be key to the information paradox in flat space as well. Along the way, we give evidence that the entanglement entropy of an ACD is a well-defined, and likely instructive, quantity. We further note that the picture of the sink we present here may have an understanding in terms of sub-matrix deconfinement in a large-$N$ setting.
We show that for the thermal spectrum of Hawking radiation black holes information loss paradox may still be present, even if including the entanglement information stored in the entangled Minkowski vacuum. And to avoid this inconsistency, the spectrum of Hawking radiation must be nonthermal. After reconsidering the derivation of Hawking effect, we find that the thermal spectrum is actually resulted from the geometric optics approximation in deriving the Bogolubov coefficients. When treated a little more accurately, we obtain some nonthermal spectrum for the Hawing radiation, which reduces to the thermal one in the geometric optics approximation.
We consider the island formula for the entropy of subsets of the Hawking radiation in the adiabatic limit where the evaporation is very slow. We find a simple concrete `on-shell formula for the generalized entropy which involves the image of the island out in the stream of radiation, the `island in the stream. The resulting recipe for the entropy allows us to calculate the quantum information properties of the radiation and verify various constraints including the Araki-Lieb inequality and strong subadditivity.
Hawking radiation of uncharged and charged scalars from accelerating and rotating black holes is studied. We calculate the tunneling probabilities of these particles from the rotation and acceleration horizons of these black holes. Using the tunneling method we recover the correct Hawking temperature as well.
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