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 spectr
um 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 show that particle production by gravitational field, especially the Hawking effect, may be treated as some quantum inertial effect, with the energy of Hawking radiation as some vacuum energy shift. This quantum inertial effect is mainly resulted
from some intrinsical energy fluctuation $hbarkappa/c$ for a black hole. In particular, there is an extreme case in which $hbarkappa/c$ is the Planck energy, giving a Planck black hole whose event horizons diameter is one Planck length. Moreover, we also provide a possibility to obtain some positive cosmological constant for an expanding universe, which is induced from the vacuum energy shift caused by quantum inertial effect.
In this paper, we try to construct black hole thermodynamics based on the fact that, the formation and evaporation of a black hole can be described by quantum unitary evolutions. First, we show that the Bekenstein-Hawking entropy $S_{BH}$ may not be
a Boltzmann or thermal entropy. To confirm this statement, we show that the original black holes first law may not simply be treated as the first law of thermodynamics formally, due to some missing metric perturbations caused by matter. Then, by including those (quantum) metric perturbations, we show that the black hole formation and evaporation can be described in a unitary manner effectively, through a quantum channel between the exterior and interior of the event horizon. In this way, the paradoxes of information loss and firewall can be resolved effectively. Finally, we show that black hole thermodynamics can be constructed in an ordinary way, by constructing statistical mechanics.
An alternative approach to decoherence, named non-dynamical decoherence is developed and used to resolve the quantum measurement problem. According to decoherence, the observed system is open to a macroscopic apparatus(together with a possible added
environment) in a quantum measurement process. We show that this open system can be well described by an almost quotient Hilbert space formed phenomenally according to some stability conditions. A group of random phase unitary operators is introduced further to obtain an exact quotient space for the observed system. In this quotient space, a density matrix can be constructed to give the Borns probability rule, realizing a (non-dynamical) decoherence. The concept of the (almost) quotient space can also be used to explain the classical properties of a macroscopic system. We show further that the definite outcomes in a quantum measurement are mainly caused by the almost quotient space of the macroscopic apparatus.
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 AMPSs 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 Hawkings 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 emph{modified quantum teleportation} to transfer the information via an EPR pairs.
