AI 中文总结
本文证明违反逆向等周不等式的AdS和dS超熵黑洞热力学不稳定，并提出超熵黑洞无平坦极限及两个更强彭罗斯不等式等猜想。
AI 中文摘要
我们提出了一系列证据，表明对于渐近反德西特（AdS）以及德西特（dS）黑洞，所 conjectured 的逆向等周不等式（RII），即 ${\cal R}_\text{RII} \ge 1$，具有根本重要性，并且其违反（${\cal R}_\text{RII} < 1$）会导致热力学不稳定性、物理上不合理的解或裸奇点。我们证明，违反逆向等周不等式的AdS黑洞，即所谓的超熵黑洞，既不满足力学稳定性要求 ${\kappa _T} \geqslant {\kappa _S} \geqslant 0$，也不满足热稳定性要求 ${C_P} \geqslant {C_V} \geqslant 0$。这一性质使得它们在全部参数空间范围内热力学不稳定，并解释了迄今为止所报道的各种不同行为。我们猜想这一陈述对所有超熵黑洞都成立。我们确认不存在超熵黑洞热力学不稳定猜想的反例，并通过呈现dS空间中超熵性的首个例子，将此猜想扩展到dS空间。通过提供证据，我们进而提出另外两个猜想：1）超熵黑洞不存在渐近平坦极限；2）对于渐近平坦黑洞，存在两个更强的彭罗斯等周不等式（PII）版本；第一个是RII的渐近平坦极限，第二个是基于ADM质量和热力学体积的新不等式，我们称之为热体积不等式，它是通过AdS扩展黑洞热力学中 $\Lambda \to 0$ 极限的洞见获得的。我们证明彭罗斯等周不等式（PII）弱于逆向等周不等式（RII），这一点在 $D=4,5$ 维以及我们所检验的所有黑洞族中得到了明确展示。
英文摘要
A collection of evidence is presented showing that the conjectured reverse isoperimetric inequality (RII) for asymptotically anti-de Sitter (AdS) as well as de Sitter (dS) black holes, ${\cal R}_\text{RII} \ge 1$, is of fundamental importance and its violation (${\cal R}_\text{RII} < 1$) gives rise to either thermodynamic instabilities, or physically unreasonable solutions, or naked singularities. We show that AdS black holes violating reverse isoperimetric inequality, known as superentropic black holes, satisfy neither mechanical stability requirement of ${κ_T} \geqslant {κ_S} \geqslant 0$ nor thermal stability requirement of ${C_P} \geqslant {C_V} \geqslant 0$. This property makes them thermodynamically unstable for the whole range of parameter space and explains all the diverse behaviors so far reported. We conjecture this statement holds for all superentropic black holes. We confirm that there is no counterexample to the thermodynamic instability conjecture of superentropic black holes and extend this to dS space by presenting the first example of superentropicity in dS space. By bringing evidence, we then propose two other conjectures: 1) there is no asymptotically flat limit of superentropic black holes, and 2) there exist two stronger versions of Penrose isoperimetric inequality (PII) for asymptotically flat black holes; the first is the asymptotically flat limit of the RII and the second is a new inequality in terms of the ADM mass and the thermodynamics volume, that we call thermo-volumetric inequality, obtained via insights from the $Λ\to 0$ limit of extended black hole thermodynamics in AdS. We show that the Penrose isoperimetric inequality (PII) is weaker than the reverse isoperimetric inequality (RII), as demonstrated explicitly for $D=4,5$ and for all black hole families we have examined.
Comments15 pages, Latex, 1 figure
