Maggiore observed that, in the high-damping regime, the quasinormal modes spectrum for the Schwarzschild black hole resembles that of a quantum harmonic oscillator. Motivated by this observation, we describe a black hole as a statistical ensemble of $N$ quantum harmonic oscillators. By working in the canonical ensemble, we show that, in the large-mass black hole limit, the leading contribution to the Gibbs entropy is the Bekenstein-Hawking term, while the subleading one is a logarithmic correction, in agreement with several results in the literature. We also find that the number of oscillators scales holographically with the area of the event horizon.

中文翻译：

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Schwarzschild 黑洞的准正规模和微观结构

Maggiore 观察到，在高阻尼状态下，Schwarzschild 黑洞的准正规模谱类似于量子谐振子的谱。受此观察的启发，我们将黑洞描述为$N$量子谐振子。通过在规范系综中工作，我们表明，在大质量黑洞极限中，对 Gibbs 熵的主要贡献是 Bekenstein-Hawking 项，而次要贡献是对数校正，这与以下几个结果一致文学。我们还发现振荡器的数量与事件视界的面积成全息比例。