We formulate spacetime inequalities applicable to quantum-corrected black holes to all orders of backreaction in semiclassical gravity. Namely, we propose refined versions of the quantum Penrose and reverse isoperimetric inequalities, valid for all known three-dimensional asymptotically anti–de Sitter quantum black holes. Previous proposals of the quantum Penrose inequality apply in higher dimensions but fail when applied in three dimensions beyond the perturbative regime. Our quantum Penrose inequality, valid in three dimensions, holds at all orders of backreaction. This suggests cosmic censorship must exist in nonperturbative semiclassical gravity. Our quantum reverse isoperimetric inequality implies a maximum entropy state for quantum black holes at fixed volume.

中文翻译：

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量子黑洞的量子不等式


我们将适用于量子校正黑洞的时空不等式表述为半经典引力中所有反作用力的阶数。也就是说，我们提出了量子彭罗斯和反向等周长不等式的改进版本，适用于所有已知的三维渐近反 de Sitter 量子黑洞。先前提出的量子彭罗斯不等式适用于更高的维度，但在扰动范围之外的三个维度上应用时失败了。我们的量子彭罗斯不等式在三维空间中有效，在所有反向反应的阶数下都成立。这表明宇宙审查必须存在于非扰动的半经典引力中。我们的量子反向等长不等式意味着量子黑洞在固定体积下的最大熵态。