Abstract
We calculate, using our recently proposed semiclassical framework, the quantum state of the Hawking pairs that are produced during the evaporation of a black hole (BH). Our framework adheres to the standard rules of quantum mechanics and incorporates the quantum fluctuations of the collapsing shell spacetime in Hawking's original calculation, while accounting for back-reaction effects. We argue that the negative-energy Hawking modes need to be regularly integrated out; and so these are effectively subsumed by the BH and, as a result, the number of coherent negative-energy modes $N_{coh}$ at any given time is parametrically smaller than the total number of the Hawking particles $N_{total}$ emitted during the lifetime of the BH. We find that $N_{coh}$ is determined by the width of the BH wavefunction and scales as the square root of the BH entropy. We also find that the coherent negative-energy modes are strongly entangled with their positive-energy partners. Previously, we have found that $N_{coh}$ is also the number of coherent outgoing particles and that information can be continually transferred to the outgoing radiation at a rate set by $N_{coh}$. Our current results show that, while the BH is semiclassical, information can be released without jeopardizing the nearly maximal inside-out entanglement and imply that the state of matter near the horizon is approximately the vacuum. The BH firewall proposal, on the other hand, is that the state of matter near the horizon deviates substantially from the vacuum, starting at the Page time. We find that, under the usual assumptions for justifying the formation of a firewall, one does indeed form at the Page time. However, the possible loophole lies in the implicit assumption that the number of strongly entangled pairs can be of the same order of $N_{total}$.
Highlights
We calculate, using our recently proposed semiclassical framework, the quantum state of the Hawking pairs that are produced during the evaporation of a black hole (BH)
We argue that the negative-energy Hawking modes need to be regularly integrated out; and so these are effectively subsumed by the BH and, as a result, the number of coherent negative-energy modes Ncoh at any given time is parametrically smaller than the total number of the Hawking particles Ntotal emitted during the lifetime of the BH
We have shown that the in-out sector of the BH radiation is close to maximally entangled; at least until the transparency time, when our perturbative analysis begins to break down
Summary
Let us give a brief account of why our framework is able to evade the firewall problem without invoking changes to the standard rules of quantum mechanics. What we have found is that the number of entangled pairs is equal to Ncoh, which is parametrically smaller than the total number of emitted particles If this possibility is realized, there must be another component that purifies the outgoing radiation during. Because information is being released as the outgoing radiation purifies, there will come a time when the rate of information release is too large for the (nearly) maximal in-out entanglement to be maintained At this point, assuming standard quantum mechanics, one could expect some large deviation of the near-horizon state from the vacuum and for the associated firewall to appear. That the Page time has, in effect, been moved to a time ttrans that is late in the evaporation process By this time, the BH can no longer be considered as semiclassical and there is no longer any good reason to expect its horizon to be a serene place (see below). Back-reaction effects from the in-falling modes become large and significant, and so the notion of a nearly classical geometry for the BH is no longer tenable
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