黑洞的统计熵

Statistical entropy of the black hole

运用量子统计的方法,直接求解Schwarzschild时空背景下玻色场和费米场的配分函数,得到熵的积分表达式.按照最近的研究结果,认为黑洞的Hawking辐射过程是隧道效应过程,在考虑黑洞隧道效应产生过程中黑洞能量发生变化的基础上,给出积分的下限为黑洞的视界位置.由此得到黑洞熵的主要项为视界面积的14.不存在使人疑惑的紫外截断因子,并且由此可得黑洞辐射粒子的能量与辐射温度成正比的结论.

Using the quantum statistical method, we directly obtain the partition function of Bose field and Fermi field on the background of Schwarzschild spacetime. The integral expression is obtained. According to the latest research results, Hawking radiation process of the black hole is a tunnel effect. During the creation of tunnel effect, the energy of the black hole changes. The lower limit of integral is the location of the black hole horizon. Therefore, the leading term of the black hole entropy is a quarter of the horizon area. In our calculation, there are no cutoffs. We obtain that the energy of the black hole radiation particle is proportional to the radiation temperature. This provides an insight into the thermodynamics and quantum property of the black hole.