By using an average heavy nuclei model, the effects of the electron screening on electron capture (EC) in core-collapse supernovae are investigated. A one-dimension code based on the Ws15M progenitor model is utilized to test the effects of electron screening during the collapsing process. The results show that, at high densities, the effects of electron screening on EC become significant. During the collapsing stage, the EC rate is decreased, the collapse time-scale is prolonged and the leakage of the neutrino energy is increased. These effects lead to an appreciable decrease in the initial energy of the bounce shock wave. The effects of electron screening in the other progenitor models are also discussed.
At the event horizon and the cosmological horizon of the stationary axisymmetricKerr-Newman black hole in the de Sitter space-time background, the tunneling rate of the charged particles is relevant with Bekenstein-Hawking entropy and the real radiation spectrum is not strictly pure thermal, but consistent with the underlying unitary theory in quantum mechanics. This is a feasible interpretation for the paradox of the black hole information loss. Taking the self-gravitation action, energy conservation, angular momentum conservation and charge conservation into account, the derived radiation spectrum is a correct amendment to the Hawking pure thermal spectrum.Kerr-Newman de Sitter black hole, energy conservation, charge conservation, angular momentum conservation, funneling rate, Bekenstein-Hawking entropyIn 1975, Hawking [1] put forward the paradox of the black hole information loss, which can cast back to the beginning of the 1970s. When no hair theorem of black hole was propounded by Carter and Robinson [2,3] , they also pointed out that most information has lost via the process of the forming of black hole, while the observer can merely study its mass, charge and angular momentum. According to the classical theory, it is relatively easy to comprehend the information loss. For it will permanently exist as a classical black hole, and there is no emitting particle at the horizon, accordingly the black hole information is considered as a conservational constant and, meanwhile, the paradox of the black hole information loss does not occur. On the contrary, the situation is changed via considering quantum effect. In 1974, Hawking proved that there exists thermal radiation in black hole with real temperature, and that its radiation spectrum is pure thermal. He held that vacuum fluctuation causes a quantum tunneling near the horizon, namely a pair of virtual particles spontaneously forms just inside the horizon: the positive energy virtual particle can tunnel out to be real particle, while the negative energy particle is absorbed by the black hole. Or particle pairs form near the outside of horizon: the negative energy virtual particle tunnels inside the ho-
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