Topology and dynamics in classical and quantum gravity

经典引力和量子引力的拓扑和动力学

基本信息

批准号：
106100-2007
负责人：
Schleich, Kristin
金额：
$ 2.49万
依托单位：
University of British Columbia
依托单位国家：
加拿大
项目类别：
Discovery Grants Program - Individual
财政年份：
2008
资助国家：
加拿大
起止时间：
2008-01-01 至 2009-12-31
项目状态：
已结题

来源：
https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=391017
关键词：
Topology dynamics classical quantum gravity

项目摘要

I am studying the interplay between topology and the dynamics of gravity of spacetimes in 3, 4 and more dimensions, both in the context of classical relativity and quantum theory. One fundamental question I would like to answer is, does our universe appear to be topologically simple because its initial quantum state made it that way or because the dynamics of general relativity force all topological structures behind black hole horizons? My earlier work on topological censorship shows small scale topological structures with nontrivial fundamental group are shrouded from outside observers in both physically reasonable, asymptotically flat and asymptotically anti de Sitter spacetimes. Thus part of the answer to this question indeed lies in the classical dynamics of topology. However, it cannot be the entire answer as the initial quantum state and quantum dynamics of gravity must produce a classical spacetime that is asymptotically flat or asymptotically anti de Sitter for topological censorship to hold. Therefore, it is also key to understand the interplay between topology and the quantum dynamics of a fundamental theory that includes gravity. Thus the dynamics of topological structures is important to our understanding of our universe at both the highest energy scales as described by a fundamental quantum theory and the lowest as described by classical relativity. Furthermore, topology may prove to be a key tool in understanding these relationships, as it is insensitive to the detailed properties of the dynamics of the quantum theory. Therefore its effects may provide a universal guide to discovering the fundamental properties of the correct high energy theory. I plan to continue research into the role topology plays in both classical relativity and in the current problems in fundamental quantum theories such as string theory and loop quantum gravity.

我正在经典相对论和量子理论的背景下研究拓扑学和 3、4 以及更多维度的时空引力动力学之间的相互作用。我想回答的一个基本问题是，我们的宇宙在拓扑上看起来很简单，是因为它的初始量子态使它如此，还是因为广义相对论的动力学迫使黑洞视界后面的所有拓扑结构？我早期关于拓扑审查的工作表明，具有非平凡基本群的小规模拓扑结构在物理合理、渐近平坦和渐近反德西特时空中都被外部观察者所掩盖。因此，这个问题的部分答案确实在于拓扑的经典动力学。然而，它不可能是完整的答案，因为初始量子态和引力的量子动力学必须产生一个渐近平坦或渐近反德西特的经典时空，才能满足拓扑审查的要求。因此，理解拓扑学和包括引力在内的基本理论的量子动力学之间的相互作用也很关键。因此，拓扑结构的动力学对于我们理解宇宙在基本量子理论所描述的最高能量尺度和经典相对论所描述的最低能量尺度上都很重要。此外，拓扑可能被证明是理解这些关系的关键工具，因为它对量子理论动力学的详细属性不敏感。因此，它的效应可以为发现正确的高能理论的基本性质提供通用指南。我计划继续研究拓扑在经典相对论和弦理论和圈量子引力等基础量子理论的当前问题中所扮演的角色。