Gibbons-Maeda dilaton 黑洞的纠缠熵

按纠缠熵方法，计算了Gibbons-Maeda(G-M)dilaton黑洞视界外部与黑洞内量子态纠缠的一薄层内量子场的统计熵，得到了G-M dilaton黑洞的Bekenstein-Hawking熵.用广义不确定原理对量子态密度进行修正，克服了brick-wall模型中视界附近态密度的发散困难，该薄层可以紧贴在事件视界上.对brick-wall外部量子场中与黑洞内自由度有关联的自由度统计熵进行了计算，并把结果与brick-wall内量子场的熵进行比较分析，显示两结果具有与视界面积成正比的一致性，但后者能更 关键词： 纠缠熵 黑洞 广义不确定原理 截断

Entanglement entropy of the Gibbons-Maeda dilaton black hole

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.