Abstract
A unitary effective field model of the black hole evaporation is proposed to satisfy almost the four postulates of the black hole complementarity (BHC). In this model, we enlarge a black hole-scalar field system by adding an extra radiation detector that couples with the scalar field. After performing a partial trace over the scalar field space, we obtain an effective entanglement between the black hole and the detector (or radiation in it). As the whole system evolves, the S-matrix formula can be constructed formally step by step. Without local quantum measurements, the paradoxes of the information loss and AMPS’s firewall can be resolved. However, the information can be lost due to quantum decoherence, as long as some local measurement has been performed on the detector to acquire the information of the radiation in it. But unlike Hawking’s completely thermal spectrum, some residual correlations can be found in the radiations. All these considerations can be simplified in a qubit model that provides a modified quantum teleportation to transfer the information via an EPR pairs.
Highlights
(iv) an in-falling observer can cross the horizon without encountering any trouble, in particular, a field vacuum can always be present in the near horizon region
It is possible to add an apparatus into the black hole evaporation problem, for example a radiation detector that couples with the scalar field
As shown in the above subsection, the black hole evaporation based on our model is unitary, how to understand Hawking’s information loss arguments? According to [1], a distant exterior observer should construct an operator like Oext, which can act only on the space generated by b†ω
Summary
In the physics of a black hole, for example, a Schwarzschild black hole with a mass M , there are mainly two classes of observers: one class consists of the distant observers, or more generally static observers, while the other one is composed of the in-falling observers. This is analogous to the arguments of reference [8], resolving the firewall paradox effectively by adding an ancillary Hilbert space By treating this ancillary Hilbert space just as the one for the interior modes, the descriptions of the static and in-falling observers may be consistent with each other, and the principle of general covariance may be obeyed.. In acquiring the correlations of (2.5), local measurements can be performed in principle while the comparison cannot be achieved because of the causal disconnectedness of the exterior and interior of a black hole This means that the “super-observer” {Oext, Oint} can not be realized physically, which may be treated as another (stronger) version of information loss. This is such a crucial extension that an effective field model can be proposed to satisfy the extended BHC(i)(ii’)(iii)(iv), so that the black hole can evaporate completely in a (effective) unitary manner
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