带帽黑洞的非唯一性：大泡与小泡
Nonuniqueness of capped black holes: large and small bubbles
AI总结：
本文提出五维最小超引力中带帽黑洞的新四参数非BPS解，由Ehlers-Harrison变换构造，无奇异性，并揭示大泡与小泡两个分支，证明球形黑洞在带帽黑洞中也存在非唯一性。
摘要：
我们提出一个新的非BPS解，描述五维最小超引力玻色子扇区中一个渐近平坦、稳态、双轴对称的带帽黑洞。该解描述一个球形黑洞，而视界外部区域在时间切片上表现出非平凡拓扑 $[{\mathbb R}^4 \\# {\mathbb C}{\mathbb P}^2] \setminus {\mathbb B}^4$。此解将我们先前构建的三参数解推广为更一般的四参数解。为推导此解，我们结合使用Ehlers和Harrison变换，然后对解的参数施加适当的边界条件。可以证明，所得解在视界上及视界外部无曲率奇点、锥奇点、Dirac-Misner弦奇点和轨道奇点，也无闭合类时曲线。该解由四个独立的守恒荷表征——质量、两个角动量和电荷——并揭示出两个不同的分支：小泡分支和大泡分支，二者通过非守恒的局域量（如磁通或磁势）加以区分。这表明球形黑洞存在非唯一性，即使在带帽黑洞中也是如此。对于等价的守恒荷集合，我们发现大/小泡分支可以具有比Cvetič-Youm黑洞更大/更小的熵。
英文摘要：
We present a new non-BPS solution describing an asymptotically flat, stationary, bi-axisymmetric capped black hole in the bosonic sector of five-dimensional minimal supergravity. This solution describes a spherical black hole, while the exterior region of the horizon exhibits a non-trivial topology of $[{\mathbb R}^4 \# {\mathbb C}{\mathbb P}^2] \setminus {\mathbb B}^4$ on a timeslice. This solution extends our previously constructed three-parameter solution to a more general four-parameter solution. To derive this solution, we utilize a combination of the Ehlers and Harrison transformations and then impose appropriate boundary conditions on the solution's parameters. It can be shown that the resultant solution is free from curvature, conical, Dirac-Misner string and orbifold singularities, as well as closed timelike curves on and outside the horizon. Characterized by four independent conserved charges -- mass, two angular momenta, and electric charge -- this solution reveals two distinct branches: a small bubble branch and a large bubble branch, distinguished by non-conserved local quantities such as magnetic flux or magnetic potential. This shows the non-uniqueness for spherical black holes, even among capped black holes. For equivalent sets of conserved charges, we find that the large/small bubble branch can have larger/smaller entropy than the Cvetič-Youm black hole.
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