Mathematical relativity and asymptotically hyperbolic manifolds

数学相对论和渐近双曲流形

• 批准号: RGPIN-2017-04896
• 负责人: Woolgar, Eric
• 金额: $ 2.19万
• 依托单位: University of Alberta
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=633055
• 关键词: Mathematical; relativity; asymptotically; hyperbolic; manifolds

If there are two kinds of geometry generally familiar, they are the flat geometry of Euclid and the round geometry of spheres. A third kind, "saddle shaped'' hyperbolic geometry, is less familiar but was popularized by the work of the artist MC Escher. These three models represent the constant curvature geometries and exhibit maximal symmetry, looking the same in every direction and at every point. Asymptotically hyperbolic (AH) manifolds, and their close cousins the asymptotically anti-de Sitter (AAdS) spacetimes, as less symmetrical. They may be bumpy and irregular in the middle but resemble hyperbolic geometry more and more at large distances from this central region. They play an important role in the modern physics of the last 30 years. They are a natural arena for black hole thermodynamics, and appear in the AdS/CFT correspondence, which relates these geometries to quantum conformal field theory and manifests "holography'', the speculative notion that physics within a region is encoded by other physics on the boundary of that region.

如果说有两种几何大家都很熟悉的话，那就是欧几里得的平面几何和球面的圆几何。第三种，“马鞍形”双曲几何，不太熟悉，但由艺术家MC Bertler的工作推广。这三个模型代表了常曲率的几何形状，并表现出最大的对称性，在每个方向和每个点上看起来都是一样的。渐近双曲（AH）流形，以及它们的近亲渐近反德西特（AAdS）时空，对称性较低。它们的中间可能是凹凸不平和不规则的，但在离这个中心区域很远的地方，它们越来越像双曲几何。它们在过去30年的现代物理学中起着重要的作用。它们是黑洞热力学的天然竞技场，出现在AdS/CFT对应中，将这些几何与量子共形场论联系起来，并体现了“全息”，即一个区域内的物理学是由该区域边界上的其他物理学编码的推测性概念。