Tunneling Effect of Two Horizons from a Reissner-Nordstrom Black Hole

Abstract

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 90β, 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 (ΔS BH ), and there is no information loss.