The criteria for thermal stability of a most general quantum black hole derived by us appeared in the form of a series of inequalities connecting second-order derivatives of black hole mass with respect to its parameters, which determine the mass of the black hole. These nullify the concept of positivity of specific heat as the sole criteria for thermal stability. Using this most general stability criterion, we prove here that AdS Schwarzschild black holes are no longer stable anywhere in their parameter space if cosmological constant is allowed to vary. We also calculate the fluctuations of both horizon area and cosmological constant of this black hole. We calculate specific heat of it and compare this with Hawking’s prediction.

中文翻译：

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垂死的 AdS 史瓦西黑洞

我们推导出的最一般的量子黑洞的热稳定性标准以一系列不等式的形式出现，这些不等式连接了黑洞质量关于其参数的二阶导数，这些参数决定了黑洞的质量。这些都否定了将比热的正性作为热稳定性的唯一标准的概念。使用这个最一般的稳定性标准，我们在这里证明，如果宇宙常数允许变化，AdS Schwarzschild 黑洞在其参数空间的任何地方都不再稳定。我们还计算了这个黑洞视界面积和宇宙常数的波动。我们计算它的比热并将其与霍金的预测进行比较。