论文标题
引力吴杨单孔
Gravitational Wu-Yang Monopoles
论文作者
论文摘要
我们表明，在可以定义S-矩阵的渐近平坦空间中，双重译本使其所有矩阵元素不变，而渐近状态的希尔伯特空间则将其分配为不同的超级选择扇区，并由其双重超压力电荷标记。这些结果表明，双重超倾斜可以解释为渐近平坦的冗余量规对称性。这将允许将一般相对论作为具有额外渐近规对称性的差异理论。然后，我们使用猜想的双倾精量规对称性来构建与Wu-Yang单极溶液的重力同等。描述解决方案的度量是使用天体球上的两个重叠贴片来定义的。该解决方案在每个斑块中分别是常规的，并且在重叠区域中可区分，其中两个描述凭借双重超级倾斜度量规变换是相同的。我们的构建提供了Misner对Taub-Nut指标的解释的替代方法。 In particular, we find that using our approach the Taub-NUT metric can be made regular everywhere on the celestial sphere and at the same time it is devoid of closed timelike curves, provided that the bound $\frac{m}{\ell} \leq \sqrt{\frac{5}{27}}$ on the ratio of mass to NUT charge is obeyed.
We show that in an asymptotically flat space where an S-Matrix can be defined, dual supertranslations leave all its matrix elements invariant and the Hilbert space of asymptotic states factorizes into distinct super-selection sectors, labeled by their dual supertranslation charges. These results suggest that dual supertranslation may be interpreted as a redundant gauge symmetry of asymptotically flat spacetimes. This would allow to recast general relativity as a theory of diffeomorphisms possessing an additional asymptotic gauge symmetry. We then use the conjectured dual supertranslation gauge symmetry to construct a gravitational equivalent of the Wu-Yang monopole solution. The metric describing the solution is defined using two overlapping patches on the celestial sphere. The solution is regular on each one of the patches separately and differentiable in the overlap region, where the two descriptions are identical by virtue of a dual supertranslation gauge transformation. Our construction provides an alternative to Misner's interpretation of the Taub-NUT metric. In particular, we find that using our approach the Taub-NUT metric can be made regular everywhere on the celestial sphere and at the same time it is devoid of closed timelike curves, provided that the bound $\frac{m}{\ell} \leq \sqrt{\frac{5}{27}}$ on the ratio of mass to NUT charge is obeyed.
