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The Doppler effect of the neutrino oscillation length in the flat space is discussed. When the observer travels away from the source, the oscillation length decreases. Moreover, the mass neutrino oscillation in the Robertson-Walker metric is studied, and the general equations of the oscillation phases are given. We obtain the relation between the phase and the scale factor. The expansion of the universe leads to the reduction of the oscillation length (blue shift), which is contrary to the red shift of the light ray. [ABSTRACT FROM AUTHOR]

The mass neutrino interference phase in a global monopole space time along the null trajectory and the geodesic is studied, and we find that the conserved energy changes a factor when a particle travels along the geodesic, if compared with the energy in the space time without the global monopole. The oscillation phase is increased by a factor due to the correction of the global monopole, comparing with the case in Schwarzschild space time. We obtain that the type-I phase along both the null and geodesic has a difference of a factor of 1−8 π η2, and that the phase along the geodesic is the double of that along the null. [ABSTRACT FROM AUTHOR]

In this paper, we study the thermal properties of the inner horizon of a Kerr-Newman black hole. By adopting Damour-Ruffini method and the thin film model which is developed on the base of brick wall model suggested by ’t Hooft, we calculate the temperature and the entropy of the inner horizon of a Kerr-Newman black hole. We conclude that the temperature of inner horizon is positive and the entropy of the inner horizon is proportional to the area of the inner horizon. The cut-off factor is same as it in calculation of the entropy of the outer horizon, 90 β. In addition, we write the integral and differential Bekenstein-Smarr formula as the parameters of the inner horizon. Then, we discuss that if the contribution of the inner horizon is taken into account to the total entropy of the black hole, the Nernst theorem can be satisfied. At last, We calculate the tunneling rate of the outer horizon Γ+ and the inner horizon Γ−. The total tunneling rate Γ should be the product of the rates of the outer and inner horizon, Γ=Γ+⋅Γ−. We find that the total tunneling rate is in agreement with the Parikh’s standard result, Γ→exp (Δ S BH), and there is no information loss. [ABSTRACT FROM AUTHOR]

The understanding of possible role played by the inner horizon of black holes in black hole thermodynamics is still somewhat incomplete. By adopting Damour-Ruffini method and the thin film model which is developed on the base of brick wall model suggested by ’t Hooft, we calculate the temperature and the entropy of the inner horizon of a R-N black hole. We conclude that the temperature of inner horizon is positive and the entropy of the inner horizon is proportional to the area of the inner horizon. In addition, the cut-off factor is 90 β, which is same in calculation of the entropy of the outer horizon. So, we prove the existence of thermal characters of the inner horizon. Then, we discuss that if the contribution of the inner horizon is taken into account to the total entropy of the black hole, the Nernst theorem can be satisfied. At last, we study the tunneling effect including the inner horizon of the Reissner-Nordstrom black hole. We calculate the tunneling rate of the outer horizon Γ+ and the inner horizon Γ−. The total tunneling rate Γ should be the product of the rates of the outer and inner horizon, Γ=Γ+⋅Γ−. We find that the total tunneling rate is in agreement with the Parikh’s standard result, Γ→exp (Δ S BH), and there is no information loss. [ABSTRACT FROM AUTHOR]

In this paper, by using well-known Eddington–Finkelstein coordinates instead of Painlevè coordinates, we study the tunneling effect of black holes. As examples of special static black holes, we calculate the tunneling rates of Gibbon–Maeda black holes. The result obtained by adopting Eddington–Finkelstein coordinates is in agreement with the Parikh’s standard result, Γ∼exp (−2Im S), which adopts the Painlevè coordinates. In addition, we discuss carefully the condition that the coordinates system in which we study the tunneling process should satisfy. In our opinion, the terms of the tunneling effect are not as strict as ones in Parikh’s paper and could be softened properly. [ABSTRACT FROM AUTHOR]