Boltzmannian state counting for black hole entropy in causal set theory,Physical Review D

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Boltzmannian state counting for black hole entropy in causal set theory
Physical Review D ( IF 4.6 ) Pub Date : 2024-07-16 , DOI: 10.1103/physrevd.110.026015
Vid Homšak ₁ , Stefano Veroni ₁

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This paper presents the first numerical study of black hole thermodynamics in causal set theory, focusing on the entropy of a Schwarzschild black hole as embodied in the distribution of proposed horizon molecules. To simulate causal sets we created a highly parallelized computational framework in c++ which allowed for the generation of causal sets with over a million points, the largest causal sets in a nonconformally flat spacetime to date. Our results confirm that the horizon molecules model is consistent with the Bekenstein-Hawking formula up to a dimensionless constant that can be interpreted as the fundamental discreteness scale in the order of a Planck length. Furthermore, the molecules are found to straddle the horizon of the black hole to within a few Planck lengths, indicating that entropy lives on the surface of the black hole. Finally, possible implications for the information paradox are drawn. In particular, we show how the horizon molecules model could yield a finite black hole temperature cutoff or even prevent full black hole evaporation.

中文翻译：

因果集理论中黑洞熵的玻尔兹曼状态计数

本文提出了因果集合论中黑洞热力学的首次数值研究，重点关注在所提出的视界分子分布中体现的史瓦西黑洞的熵。为了模拟因果集，我们在 C++ 中创建了一个高度并行化的计算框架，该框架允许生成具有超过一百万个点的因果集，这是迄今为止非共形平坦时空中最大的因果集。我们的结果证实，地平线分子模型在无量纲常数范围内与贝肯斯坦-霍金公式一致，该常数可以解释为普朗克长度量级的基本离散尺度。此外，这些分子被发现跨越黑洞的视界，距离在几个普朗克长度之内，这表明熵存在于黑洞的表面。最后，得出了信息悖论的可能含义。特别是，我们展示了地平线分子模型如何产生有限的黑洞温度截止值，甚至防止黑洞完全蒸发。

更新日期：2024-07-17

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