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砖墙模型不能给出黑洞熵
The brick-wall model unapplicable to the calculating of black hole entropy
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摘要: 砖墙模型被广泛用于静态或稳态黑洞熵的计算,但为了避免发散,砖墙模型需要引入一紫外截断因子.截断因子的引入至今没有给以合理的解释.有工作表明,用砖墙模型或薄膜模型计算黑洞熵时,若采用广义不确定关系则可以去掉截断因子.证明了将广义不确定关系用于砖墙模型计算Schwarzschild黑洞熵时,由于砖墙模型给出熵的第一项既是Bekenstein-Hawking项又含有截断因子,因此在去掉截断因子的同时也丢掉了Bekenstein-Hawking项,将得不到黑洞熵.Abstract: The brick-wall model is widely used to calculate the entropies of static or stationary black holes.An ultraviolet cutoff factor needs to be introduced to remove the divergence of the result in brick-wall model.The cutoff factor has not been explained reasonably up to now.A study indicated that when the brick-wall model or thin film model was used to calculate the black hole entropy,the ultraviolet cutoff factor could be discarded if the generalized uncertainty relation was adopted.In this paper,it is proved that since the first term of Schwarzschild black hole entropy formula in the brick-wall model is not only the Bekenstein-Hawking term but also the term containing the ultraviolet cutoff factor,when the cutoff factor is removed,the Bekenstein-Hawking term is lost and the black hole entropy cannot be obtained by using the generalized uncertainty relation in brick-wall model.
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