AI 中文总结
该研究推导了极端Reissner–Nordström黑洞形成时标量电荷需满足的界限，对比得出亚极端坍缩无此类界限，补充了Schwarzschild黑洞成为极端黑洞的条件，为真空黑洞力学第三定律不成立提供了证据。
AI 中文摘要
我证明，形成精确极端Reissner–Nordström黑洞（遵循Kehle–Unger方案）、半径为$r_+$的坍缩带电标量场，其标量电荷$\boldsymbol{\frak{e}}$必须满足$|\boldsymbol{\frak{e}}|r_+ > \frac{1}{3}$。与之相对，我还表明亚极端坍缩不存在此类界限：任意$\boldsymbol{\frak{e}} \ne 0$的标量场可形成具有任意（亚极端）荷质比的亚极端黑洞。作为极端界限的补充，我证明若$|\boldsymbol{\frak{e}}|r_+ > \boldsymbol{\frac{3 + \boldsymbol{\frak{33}}}{3}}$，Schwarzschild黑洞可成为极端黑洞。$|\boldsymbol{\frak{e}}|r_+$可取量级为1的事实，可视为真空黑洞力学第三定律不成立的证据。
英文摘要
I prove that a collapsing charged scalar field with scalar charge $\mathfrak{e}$ that forms an exactly extremal Reissner--Nordström black hole à la Kehle--Unger with radius $r_+$ must satisfy $|\mathfrak{e}|r_+ > \frac{1}{3}$. In contrast, I also show that no such bound exists for subextremal collapse: a scalar field with an arbitrary $\mathfrak{e} \ne 0$ can form a subextremal black hole with an arbitrary (subextremal) charge-to-mass ratio. Complementing the extremal bound, I prove that a Schwarzschild black hole can become extremal if $|\mathfrak{e}|r_+ > \sqrt{\frac{3 + \sqrt{33}}{3}}$. The fact that $|\mathfrak{e}|r_+$ can be taken to be of order unity could be considered evidence that the third law of black hole mechanics in vacuum is false.
Comments15 pages, 1 figure
