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arXiv 0709.1812gr-qc
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黑洞热力学的玻尔半经典模型

A Bohr's Semiclassical Model of the Black Hole Thermodynamics

V. Pankovic, M. Predojevic, P. Grujic

摘要:

我们提出了一个简单的程序来评估史瓦西黑洞的主要物理属性:贝肯斯坦-霍金熵,霍金温度和贝肯斯坦量子化的表面积。利用黑洞视界上一个大圆的周长包含有限个相应的约化康普顿波长的条件。它本质上类似于玻尔原子模型中的玻尔量子化假设,用德布罗意关系解释。我们提出的黑洞辐射的形式在概念上类似于玻尔的假设的离散量子跳跃的电子在旧的量子理论的光子发射。它使我们能够根据海森堡的测不准关系和玻尔的对应原理对黑洞蒸发的时间间隔作一个粗略的估计,结果与标准霍金理论所预言的时间间隔非常接近。我们的计算证实了贝肯斯坦的能量量子化的半经典结果,与弗拉斯卡(2005)的计算不同。最后,我们推测了可能的源能量分布在黑洞视界。

英文摘要:

We propose a simple procedure for evaluating the main thermodynamical attributes of a Schwarzschild's black hole: Bekenstein-Hawking entropy, Hawking's temperature and Bekenstein's quantization of the surface area. We make use of the condition that the circumference of a great circle on the black hole horizon contains finite number of the corresponding reduced Compton's wavelength. It is essentially analogous to Bohr's quantization postulate in Bohr's atomic model interpreted by de Broglie's relation. We present black hole radiation in the form conceptually analogous to Bohr's postulate on the photon emission by discrete quantum jump of the electron within the Old quantum theory. It enables us, in accordance with Heisenberg's uncertainty relation and Bohr's correspondence principle, to make a rough estimate of the time interval for black hole evaporation, which turns out very close to time interval predicted by the standard Hawking's theory. Our calculations confirm Bekenstein's semiclassical result for the energy quantization, in variance with Frasca's (2005) calculations. Finally we speculate about the possible source-energy distribution within the black hole horizon.

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