Entanglement entropy of the Gibbons-Maeda dilaton black hole

Abstract

By using the entanglement entropy method, in the Gibbons-Maeda(G-M) dilaton space-time, the statistical entropy of the quantum field in a thin film is calculated and the Bekenstein-Hawking entropy of the G-M dilaton black hole is obtained.Here, the quantum field is entangled with the quantum states in the black hole and the thin film sticks to the event horizon from outskirt of the black hole.Taking into account the effect of the generalized uncertainty principle on the quantum state density, the difficulty of the divergence of the state density near the event horizon in the brick-wall model is removed.Calculating the statistical entropy of the degrees of freedom entangling to the quantum states in the black hole in the quantum field outside the brick-wall and comparing the result to the entropy from the degrees of freedom inside brick-wall, we see that the two results are consistent but the latter may embody preferably the essence of black hole entropy.Using the residue theorem, the integration difficulty in he calculation is overcome and the result of the paper is founded quantitatively. These calculation and discussion imply that the high density quantum states near the event horizon are strongly correlated with the quantum states in black hole and the ultraviolet cut-off in the brick-wall model is not reasonable. The quantization of gravity field should be considered in the high energy quantum field near the event horizon and the ultraviolet cut-off is not necessary. In the quantum field inside and outside the brick-wall, the degrees of freedom contributing to the black hole entropy are just those correlating with the degrees of freedom in the black hole.