Gibbons-Maeda dilaton黑洞的纠缠熵

Entanglement entropy of the Gibbons-Maeda dilaton black hole

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-Mdilaton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,但后者能更好地反映黑洞熵的本质.利用留数定理,克服了计算中的积分困难,所得的结论是定量成立的.计算和讨论表明:黑洞事件视界外部附近的高密度量子态与黑洞内部有强关联,brick-wall模型中的紫外截断是不合理的.在视界附近的高能态量子场中,应当考虑引力场的量子化效应,brick-wall模型中的紫外截断也是不必要的.在brick-wall内外的量子场中,对黑洞熵有贡献的均是与黑洞内部量子态有关联的自由度.

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 the 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.