Tunnelling Effect of Two Horizons from a Gibbons--Maeda Black Hole

We study the thermal characters of the inner horizon of a Gibbons--Maeda black hole. In order to satisfy the Nernst theorem of the third law, the entropy of the black hole with two horizons must depend not only on the area of the outer horizon but also on the area of the inner horizon. Then the temperature of the inner horizon is calculated. Lastly, the tunnelling effect including the inner horizon of a Gibbons--Maeda black hole is investigated. We also calculate the tunnelling rate of the outer horizon Γ₊ and the inner horizon Γ_-. The total tunnelling rate Γ should be the product of the rates of the outer and inner horizon, Γ=Γ₊.Γ_-. It is found that the total tunnelling rate is in agreement with the Parikh's standard result, Γ→exp(∆S_BH), and there is no information loss.