黑洞的宽度参数和内部结构
The Width Paradox and the Internal Structure of a Black-Hole
摘要：
在黑洞热力学的早期，贝肯斯坦计算了宏观黑洞的质量色散，这是由它发射的热辐射的随机性引起的--对于质量比$M \stackrel{>}{\sim} 10^{30}g$大的黑洞，它被证明是负的。他将其命名为{ \it“质量宽度悖论”}。在这里，我们重温他的早期计算，在一个公理化的方法与一组更经济的假设，并得出类似的结论。我们认为，质量悖论的结果考虑一个黑洞作为一个经典系统，没有内部的量子结构。事实上，当我们考虑到区域能级的离散性，并假设相邻量子态\cite{bekenstein}之间的跃迁概率相等时，这个悖论就消失了。在这个过程中，我们得到了在给定平均面积的本征态中发现黑洞的概率。作为一个副产品，量子方案也指向一个可能的解决方案的黑洞信息难题。
英文摘要：
In the early days of Black Hole Thermodynamics, Bekenstein calculated the mass dispersion of a macroscopic black hole that results from the stochasticity of the thermal radiation it emits -- it turned out to be negative for black holes massive than $M \stackrel{>}{\sim} 10^{30}g$. He named it the {\it "mass width paradox"}. Here we revisit his early calculation, in an axiomatic approach with a set of more economical assumptions and reach similar conclusions. We argue that the mass paradox results from considering a black hole as a classical system, without an inner quantum structure. As a matter of fact, when we take into account the discreteness of the area levels and assume identical probability transition between contiguous quantum states \cite{bekenstein}, the paradox disappears. In the process we obtain the probability of finding a black-hole in some area eigenstate for a given averaged area. As a by-product, the quantum scenario also points towards a possible solution of the black hole information conundrum.
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