黑洞热力学第三定律与标量场的质荷比
The third law of black hole thermodynamics and the mass-to-charge ratio of scalar fields
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中文总结 AI 辅助
本文基于量子效应推测Reall界限不尖锐，提出在特定质荷比范围内真空极化产生粒子对使黑洞放电，从而确保热力学第三定律的量子有效性，并加强经典界限以阻止极端Reissner-Nordström黑洞动态形成。
中文摘要 AI 辅助
Kehle和Unger最近证明，自引力带电经典标量场可以在有限时间内坍缩形成极端Reissner-Nordström（eRN）黑洞，从而违反热力学第三定律（TLT）。Reall随后证明，如果场的质荷比超过1，即$m/e\geq1$，则在引力坍缩中形成eRN黑洞是不可能的。在本紧凑论文中，我们基于量子考虑推测Reall界限并非尖锐的。特别地，我们指出，在$(eQ/\hbar)^2>(mQ/\hbar)^2+1/4$的范围内，电荷为$Q$的带电系统的电场将自发极化真空，从而产生带电粒子对，这些粒子对会使黑洞放电，并在此范围内确保TLT的量子有效性。受TLT的启发，我们推测经典Reall界限可以被加强，使得在$m/e\geq\sqrt{1-({{\hbar}/{2eQ}})^2}$的范围内，经典考虑将阻止eRN黑洞动态形成，而在此范围内量子极化效应无法保护TLT。
英文摘要
Kehle and Unger have recently shown that self-gravitating charged classical scalar fields can collapse to form extremal Reissner-Nordström (eRN) black holes in finite time, thus violating the third law of thermodynamics (TLT). Reall has subsequently proved that the formation of an eRN black hole in gravitational collapse is impossible if the mass-to-charge ratio of the field exceeds unity, $m/e\geq1$. In the present compact paper we conjecture, using quantum considerations, that the Reall bound is {\it not} sharp. In particular, we point out that the electric field of a charged system with charge $Q$ will spontaneously polarize the vacuum in the regime $(eQ/\hbar)^2>(mQ/\hbar)^2+1/4$, thereby creating pairs of charged particles that discharge the black hole and ensure the quantum validity of the TLT in this regime. Motivated by the TLT, we conjecture that the classical Reall bound can be strengthened such that classical considerations would prevent eRN black holes from forming dynamically in the regime $m/e\geq\sqrt{1-\big({{\hbar}/{2eQ}}\big)^2}$, where quantum polarization effects are unable to protect the TLT.
发表机构
- The Ruppin Academic Center（鲁平学术中心）
- Racah Institute of Physics, The Hebrew University（拉卡赫物理研究所，希伯来大学）
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