Topology and dynamics in classical and quantum gravity

经典引力和量子引力的拓扑和动力学

• 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: 2007
• 资助国家: 加拿大
• 起止时间: 2007-01-01 至 2008-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=362368
• 关键词: Topology; dynamics; classical; quantum; gravity

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.

在经典相对论和量子理论的背景下，我正在研究3、4和更多维度时空的拓扑和引力动力学之间的相互作用。我想回答的一个基本问题是，我们的宇宙在拓扑结构上看起来简单是因为它的初始量子态造成的还是因为广义相对论的动力学迫使所有的拓扑结构都在黑洞视界后面？我在拓扑审查方面的早期工作表明，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存在于拓扑学的经典动力学中。然而，它不可能是全部答案，因为引力的初始量子态和量子动力学必须产生一个经典时空，它是渐近平坦的或渐近反德西特的，以使拓扑审查保持不变。因此，理解包括引力在内的基本理论的拓扑和量子动力学之间的相互作用也是关键。因此，无论是在基本量子理论所描述的最高能量尺度上，还是在经典相对论所描述的最低能量尺度上，拓扑结构的动力学对于我们理解宇宙都是很重要的。此外，拓扑学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特性不敏感。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一个普遍的指导。我计划继续研究拓扑学在经典相对论中所扮演的角色，以及在基础量子理论（如弦理论和环量子引力）中当前存在的问题。