从可积性看稳态真空黑洞的模空间

IF 1 4区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL Advances in Theoretical and Mathematical Physics Pub Date : 2020-08-28 DOI:10.4310/ATMP.2022.v26.n2.a4
James Lucietti, Fred Tomlinson
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引用次数: 4

摘要

我们考虑了四维和五维的渐近平坦、平稳、真空黑洞时空的分类,它们分别允许一个和两个交换轴向杀伤场。众所周知,爱因斯坦方程可化为二维轨道空间上的调和映射,这本身就是线性谱方程系统的可积性条件。我们沿着轨道空间的边界对Belinski-Zakharov谱方程进行积分,并利用它来完全确定轴和视界上的度规势和相关的恩斯特势和扭转势。对于任何给定的杆结构,这足以导出在轴上不存在圆锥奇点的解的模空间。作为该方法的一个例子,我们获得了Kerr黑洞和Myers-Perry黑洞以及已知的双自旋黑环的构造唯一性证明。
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Moduli space of stationary vacuum black holes from integrability
We consider the classification of asymptotically flat, stationary, vacuum black hole spacetimes in four and five dimensions, that admit one and two commuting axial Killing fields respectively. It is well known that the Einstein equations reduce to a harmonic map on the two-dimensional orbit space, which itself arises as the integrability condition for a linear system of spectral equations. We integrate the Belinski-Zakharov spectral equations along the boundary of the orbit space and use this to fully determine the metric and associated Ernst and twist potentials on the axes and horizons. This is sufficient to derive the moduli space of solutions that are free of conical singularities on the axes, for any given rod structure. As an illustration of this method we obtain constructive uniqueness proofs for the Kerr and Myers-Perry black holes and the known doubly spinning black rings.
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来源期刊
Advances in Theoretical and Mathematical Physics
Advances in Theoretical and Mathematical Physics 物理-物理:粒子与场物理
CiteScore
2.20
自引率
6.70%
发文量
0
审稿时长
>12 weeks
期刊介绍: Advances in Theoretical and Mathematical Physics is a bimonthly publication of the International Press, publishing papers on all areas in which theoretical physics and mathematics interact with each other.
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