论文标题
通过Morse功能进行拓扑变化：Borde-Sorkin猜想的进展
Topology change with Morse functions: progress on the Borde-Sorkin conjecture
论文作者
论文摘要
拓扑变化被某些作者认为是量子重力的必要特征，而其他作者则是不可能的。反对它的主要论点之一是，空间拓扑变化的空间具有不良的因果特性。 Borde和Sorkin提出了一种避免这种困境的方法，即考虑拓扑改变了从Morse函数构建的空间，在该空间中允许该指标在孤立的点消失。他们猜想这些摩尔斯空间是有因果关系的（因此表现得很好），只要莫尔斯点的索引与$ 1 $和$ n-1 $不同。在本文中，我们证明了这种猜想的特殊情况。我们还启发性地认为，原始猜想实际上是错误的，并制定了它的精制版本。
Topology change is considered to be a necessary feature of quantum gravity by some authors, and impossible by others. One of the main arguments against it is that spacetimes with changing spatial topology have bad causal properties. Borde and Sorkin proposed a way to avoid this dilemma by considering topology changing spacetimes constructed from Morse functions, where the metric is allowed to vanish at isolated points. They conjectured that these Morse spacetimes are causally continuous (hence quite well behaved), as long as the index of the Morse points is different from $1$ and $n-1$. In this paper, we prove a special case of this conjecture. We also argue, heuristically, that the original conjecture is actually false, and formulate a refined version of it.
