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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 isla
Hawking radiation is obtained from anomalies resulting from a breaking of diffeomorphism symmetry near the event horizon of a black hole. Such anomalies, manifested as a nonconservation of the energy momentum tensor, occur in two different forms -- c
Hawking radiation of the blackhole is calculated based on the principle of local field theory. In our approach, the radiation is a unitary process, therefore no information loss will be recorded. In fact, observers in different regions of the space c
We comment on the consistence of the epsilon anti-symmetric tensor adopted in [R. Banerjee and S. Kulkarni, arXiv:0707.2449] when it is generalized in the general case where $sqrt{-g} eq 1$. It is pointed out that the correct non-minimal consistent
By entangling soft massless particles one can create an arbitrarily large amount of entanglement entropy that carries an arbitrarily small amount of energy. Dropping this entropy into the black hole (b.h.) one can increase the b.h. entropy by an amou