论文标题
扭曲溶液的全球性质与电磁场的一般相对论和宇宙常数。 ii
Global properties of warped solutions in General Relativity with an electromagnetic field and a cosmological constant. II
论文作者
论文摘要
我们考虑使用最小耦合到电磁场的宇宙恒定的一般相对性，并假设四维时空歧管是带有Lorentzian和Euclidean签名指标的两个表面的扭曲产物。场方程表明，至少一个表面必须具有恒定的曲率，导致指标的对称性（``自发对称出现''）。在Lorentzian表面具有恒定曲率的情况下，我们对所有全局解决方案进行了分类。相对于在洛伦兹表面上作用的Lorentz So（1,2）或Poincare IO（1,1）组，这些解决方案是不变的。
We consider general relativity with cosmological constant minimally coupled to the electromagnetic field and assume that the four-dimensional space-time manifold is a warped product of two surfaces with Lorentzian and Euclidean signature metrics. Field equations imply that at least one of the surfaces must be of constant curvature leading to the symmetry of the metric (``spontaneous symmetry emergence''). We classify all global solutions in the case when the Lorentzian surface is of constant curvature. These solutions are invariant with respect to the Lorentz SO(1,2) or Poincare IO(1,1) groups acting on the Lorentzian surface.
