论文标题
BACH方程和在保形循环宇宙学模型中的空间匹配
Bach equation and the matching of spacetimes in conformal cyclic cosmology models
论文作者
论文摘要
我们考虑了在保形循环宇宙学模型中匹配两个空间的问题，即先前和现在的Aeons。它们之间的共同边界继承了两组约束 - 爱因斯坦磁场方程的每个解决方案都延伸至保形边界。假定以前的AEON是渐近的Sitter时空，因此爱因斯坦田间方程的标准形式足以从未来的无效无穷大。对于应该从最初的奇异性演变而来的未来的Aeon，它们是通过使用Bach方程来获得的。该方程式在过去的保形无穷大范围内是常规的，对于爱因斯坦的固定时间和共形，因此我们将主要关注它们。附录中将讨论电动汽车时空的一个示例，该示例不属于此类且具有常规的保形BACH张量。
We consider the problem of matching two spacetimes, the previous and present aeons, in the Conformal Cyclic Cosmology model. The common boundary between them inherits two sets of constraints -- one for each solution of the Einstein field equations extended to the conformal boundaries. The previous aeon is assumed to be an asymptotically de Sitter spacetime, so the standard conformal formulation of the Einstein field equations suffice to derive the constraints on the future null infinity. For the future aeon, which is supposed to evolve from an initial singularity, they are obtained with the use of the Bach equation. This equation is regular at the past conformal infinity for conformally flat and conformally Einstein spacetimes, so we will mostly focus on them here. An example of the electrovacuum spacetime which does not fall into this class and has regular conformal Bach tensor will be discussed in the appendix.
