论文标题
幻影标量字段困扰的静态空间：无质量的分类和全球结构
Static spacetimes haunted by a phantom scalar field: classification and global structure in the massless case
论文作者
论文摘要
我们讨论了$ n（\ ge 4）$ - 维空间的各种新颖特征，该空间由一般相对论中的无质量（非）幻影标量场提供。假设该度量是静态二维Lorentzian时空的扭曲产物和$（N-2）$ - 尺寸的Einstein Space $ k^{n-2} $，曲率$ k = 0，\ pm 1 $，并且标量球场仅取决于辐射可变，我们在辐射方面都呈现出刻有态度的分类。与非平势标量场的情况相反，Fisher溶液并非唯一，并且存在两个与Ellis-Gibbons溶液和Ellis-Bronnikov解决方案的概括相对应的其他指标。我们通过分析空/间距类的大地测量和奇异性来详细探讨这些解决方案的最大扩展。对于幻影Fisher和Ellis-Gibbons的解决方案，我们发现在没有标量曲率奇点的参数区域中，不可避免地会出现平行（P.P）曲率奇异性。有趣的是，这些P.P曲率奇异性在沿着径向null测量学沿线的有限仿射时间内访问。因此，只有Ellis-Bronnikov溶液描述了在两侧渐近平坦的时空中的常规虫洞。使用与爱因斯坦和约旦框架有关的一般转换，我们还提供了与同一对称性耦合到共形标量场的完全分类。此外，通过求解约旦框架中的字段方程，我们证明了这种分类是真正完整的。
We discuss various novel features of $n(\ge 4)$-dimensional spacetimes sourced by a massless (non-)phantom scalar field in general relativity. Assuming that the metric is a warped product of static two-dimensional Lorentzian spacetime and an $(n-2)$-dimensional Einstein space $K^{n-2}$ with curvature $k=0, \pm 1$, and that the scalar field depends only on the radial variable, we present a complete classification of static solutions for both signs of kinetic term. Contrary to the case with a non-phantom scalar field, the Fisher solution is not unique, and there exist two additional metrics corresponding to the generalizations of the Ellis-Gibbons solution and the Ellis-Bronnikov solution. We explore the maximal extension of these solutions in detail by the analysis of null/spacelike geodesics and singularity. For the phantom Fisher and Ellis-Gibbons solutions, we find that there inevitably appear parallelly propagated (p.p) curvature singularities in the parameter region where there are no scalar curvature singularities. Interestingly, the areal radius blows up at these p.p curvature singularities, which are nevertheless accessible within a finite affine time along the radial null geodesics. It follows that only the Ellis-Bronnikov solution describes a regular wormhole in the two-sided asymptotically flat spacetime. Using the general transformation relating the Einstein and Jordan frames, we also present a complete classification of solutions with the same symmetry coupled to a conformal scalar field. Additionally, by solving the field equations in the Jordan frame, we prove that this classification is genuinely complete.
