论文标题
部分可观测时空混沌系统的无模型预测
Extensions of Lorentzian Hawking--Page Solutions with Null Singularities, Spacelike Singularities, and Cauchy horizons of Taub--NUT type
论文作者
论文摘要
从鹰式解决方案开始，我们考虑相应的洛伦兹锥体指标。这些代表锥体内部尺度不变的真空溶液，在缩放起源的时间顺序上定义。我们将Lorentzian Hawking-Page解决方案扩展到$（4+1）$ - 尺寸尺度尺度不变的真空解决方案（3）\ times U（3）\ times u（1）$ ismetry，使用kaluza-kaluza-- klein降低和Christodoulou的方法。我们证明，每个Lorentzian Hawking - 页面的解决方案都具有延伸的曲率奇异性，具有空间曲率奇异性的扩展，并带有taub-taub类型的无效的Cauchy Horizon的扩展。这些都是我们对称类中的所有可能扩展。具有无效曲率奇点的间距的扩展可用于构建$（4+1）$ - 尺寸渐近平坦的真空飞机，局部赤裸裸的奇异性，其中未被捕获的表面未在无效的曲率奇点上进行。我们使用Christodoulou的蓝移效果证明了这种本地赤裸裸的奇异性的不稳定。
Starting from the Hawking--Page solutions, we consider the corresponding Lorentzian cone metrics. These represent cone interior scale-invariant vacuum solutions, defined in the chronological past of the scaling origin. We extend the Lorentzian Hawking--Page solutions to the cone exterior region in the class of $(4+1)$-dimensional scale-invariant vacuum solutions with an $SO(3)\times U(1)$ isometry, using the Kaluza--Klein reduction and the methods of Christodoulou. We prove that each Lorentzian Hawking--Page solution has extensions with a null curvature singularity, extensions with a spacelike curvature singularity, and extensions with a null Cauchy horizon of Taub--NUT type. These are all the possible extensions within our symmetry class. The extensions to spacetimes with a null curvature singularity can be used to construct $(4+1)$-dimensional asymptotically flat vacuum spacetimes with locally naked singularities, where the null curvature singularity is not preceded by trapped surfaces. We prove the instability of such locally naked singularities using the blue-shift effect of Christodoulou.
