Topology change with Morse functions: progress on the Borde–Sorkin conjecture

IF 1 4区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL
Leonardo García-Heveling
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引用次数: 0

Abstract

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.
莫尔斯函数的拓扑变化:博尔德-索金猜想的进展
一些学者认为拓扑变化是量子引力的一个必要特征,而另一些学者则认为这是不可能的。反对拓扑变化的主要论据之一是,空间拓扑变化的时空具有不好的因果特性。Borde 和 Sorkin 提出了一种避免这种困境的方法,即考虑由莫尔斯函数构造的拓扑变化的时空,允许度量在孤立点上消失。他们猜想,只要莫尔斯点的索引不同于$1$和$n-1$,这些莫尔斯时空就是因果连续的(因此表现相当好)。在本文中,我们证明了这一猜想的一个特例。我们还启发式地论证了原猜想实际上是错误的,并提出了一个完善的版本。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Advances in Theoretical and Mathematical Physics
Advances in Theoretical and Mathematical Physics 物理-物理:粒子与场物理
CiteScore
2.20
自引率
6.70%
发文量
0
审稿时长
>12 weeks
期刊介绍: Advances in Theoretical and Mathematical Physics is a bimonthly publication of the International Press, publishing papers on all areas in which theoretical physics and mathematics interact with each other.
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