标题： 黑洞蒸发的概率分布 显示英文标题

标题： Probability distribution for black hole evaporation

摘要： 如果考虑发射粒子对黑洞时空的反作用或自引力效应，则可以得到从黑洞发射粒子的非热修正概率。 这些非热发射的粒子会保持黑洞的熵不变，即黑洞完全蒸发后辐射粒子系统的熵与黑洞初始熵相匹配。 利用非热发射概率，我们已经计算出质量为$M$的黑洞被一定数量的粒子（$n$）完全蒸发的概率。 这是通过首先评估黑洞通过发射$n$数量的粒子蒸发的可能性数，然后计算黑洞总共有多少种蒸发方式来实现的。 这两个量的比值给出了所需的概率。 从概率分布中，我们得到了最可能耗尽黑洞的粒子数与初始黑洞温度之间的位移关系。 这个关系类似于黑体辐射的维恩位移定律。 显示英文摘要

摘要： Non-thermal correction to the emission probability of particles from black holes can be obtained if the backreaction or self-gravitational effects of the emitted particles on the black hole spacetime are taken into consideration. These non-thermally emitted particles conserve the entropy of the black hole, i.e, the entropy of the system of radiated particles after complete evaporation of the black hole matches the initial entropy of the black hole. Using the non-thermal emission probability, we have determined the probability for a black hole of mass $M$ to be completely evaporated by a given number of particles $n$. This is done by first evaluating the number of possible ways in which the black hole can be evaporated by emitting $n$ number of particles, and then the total number of ways in which the black hole can be evaporated. The ratio of these two quantities gives us the desired probability. From the probability distribution, we get a displacement relation between the most probable number of particles exhausting the black hole and the temperature of the initial black hole. This relation resembles Wien's displacement law for blackbody radiation.