标题： 莫尔斯指标和因果连续性。 量子引力中拓扑变化的判据 显示英文标题

标题： Morse index and causal continuity. A criterion for topology change in quantum gravity

摘要： 在1+1维中的研究表明，在量子引力中，因果不连续的拓扑变化时空被抑制。 Borde和Sorkin提出了一个猜想，即因果不连续性恰好与从Morse函数构建的拓扑变化时空中指数为1或n-1的Morse点相关。 我们确立了该猜想的一个较弱形式。 即，如果一个紧致cobordism上的Morse函数f具有指数为1或n-1的临界点，那么与f相关的所有Morse几何都是因果不连续的；而如果f没有指数为1或n-1的临界点，那么存在与之相关的因果连续的Morse几何。 显示英文摘要

摘要： Studies in 1+1 dimensions suggest that causally discontinuous topology changing spacetimes are suppressed in quantum gravity. Borde and Sorkin have conjectured that causal discontinuities are associated precisely with index 1 or n-1 Morse points in topology changing spacetimes built from Morse functions. We establish a weaker form of this conjecture. Namely, if a Morse function f on a compact cobordism has critical points of index 1 or n-1, then all the Morse geometries associated with f are causally discontinuous, while if f has no critical points of index 1 or n-1, then there exist associated Morse geometries which are causally continuous.