Letter: Quantum Entropy of the Garfinkle-Horowitz-Strominger Dilaton Black Hole

Abstract

Taking into account the effect of the generalized uncertainty principle on the equation of the density of the states, we calculate the entropy of the quantum scalar field inside the brick-wall of the Garfinkle-Horowitz-Strominger dilaton black hole. The entropy proportional to the event horizon area is obtained without any cutoff. Compared to the entropy from the outside of the brick-wall, the two results are similar. This implies that the quantum theory of gravity can remove the divergence of the state density on the event horizon and avoid the cut-off in the original brick-wall model.