黑洞热力学第三定律：量子与经典考量
The third law of black hole thermodynamics: Quantum versus classical considerations
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- The Ruppin Academic Center（鲁平学术中心）
- Racah Institute of Physics, The Hebrew University（希伯来大学雷卡物理研究所）
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中文总结 AI 辅助
本文探讨黑洞热力学第三定律，指出量子真空极化效应可保证极端黑洞不形成，并推测经典界限可加强至$|eQ|<\hbar/2$以维持该定律。
中文摘要 AI 辅助
Kehle和Unger最近证明，在适当条件下，无质量带电经典标量场可以在有限时间内产生极端黑洞。这一结果似乎违反了热力学第三定律（TLT），因为极端黑洞的温度为零。然而，由于TLT本质上是一个量子原理，对这一问题的自洽分析必须考虑量子效应。特别是，我们指出系统的电场可能自发极化真空，从而产生无质量带电粒子对，这些粒子对将使黑洞放电。这一机制保证了在$|eQ|\geq\hbar/2$区域（此处${Q,e}$分别表示黑洞和标量场的电荷）TLT的{\it 量子}有效性。这留下了对于$|eQ|/\hbar$较低值时会发生什么的问题。最近，Schneider推导出一个经典界限，表明在$|eQ|\leq\hbar/3$的小电荷区域，极端黑洞不能以Kehle-Unger方式形成。他的分析留下了可能存在更强界限的可能性。我们在此推测，这一界限确实可以加强，使得经典考量将在$|eQ|<\hbar/2$区域阻止极端（零温度）带电Reissner-Nordström黑洞动态形成，在该区域量子极化效应太弱而无法保持TLT的有效性。
英文摘要
Kehle and Unger have recently shown that, under suitable conditions, a massless charged classical scalar field can produce an extremal black hole in finite time. This result appears to violate the third law of thermodynamics (TLT), since extremal black holes have zero temperature. However, because the TLT is intrinsically a quantum principle, a self-consistent analysis of this problem must account for quantum effects. In particular, we point out that the electric field of the system may spontaneously polarize the vacuum, thereby creating massless charged pairs that will discharge the black hole. This mechanism guarantees the {\it quantum} validity of the TLT in the regime $|eQ|\geq\hbar/2$ (here ${Q,e}$ denote, respectively, the electric charges of the black hole and the scalar field). This leaves open the question of what happens for lower values of $|eQ|/\hbar$. Recently, Schneider derived a classical bound showing that extremal black holes cannot be formed à la Kehle-Unger in the small-charge regime $|eQ|\leq\hbar/3$. His analysis leaves open the possibility that a stronger bound may exist. We conjecture here that this bound can indeed be strengthened such that classical considerations would prevent extremal (zero-temperature) charged Reissner-Nordström black holes from forming dynamically in the regime $|eQ|<\hbar/2$, where quantum polarization effects are too weak to preserve the validity of the TLT.
