Mathematical Sciences: On Some Geometric Constructions and On the Properties of the Kerr Black Hole

数学科学：关于一些几何结构和克尔黑洞的性质

• 批准号: 9704338
• 负责人: Nicolaos Kapouleas
• 金额: $ 14万
• 依托单位: Brown University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-07-01 至 2001-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9704338&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Some; Geometric; Constructions

9704338 Kapouleas The proposal consists of two somewhat distinct groups of projects. The first group of project deals with various geometric constructions by singular pertubation methods. These include constructions using desingularization of intersecting minimal surfaces, minimal hypersurfaces and constant mean curvature hypersurfaces in higher dimensional Euclidean space, and Einstein four-manifolds. The second group of projects lie in the area of general relativity. In particular, the PI, in collaboration with Christodoulou, will try to settle uniqueness and stability questions for the Kerr and Schwarzschild black holes. Minimal surfaces arise as various physical surfaces; they have the remarkable property of minimizing the surface area amongst all surfaces bounded by the same spatial contour. Minimal surfaces can also used to model condensed matter. Stability questions for black holes, which involve examining the interaction of a black hole with weak gravitational waves, have important applications in cosmology.

小行星9704338 该提案包括两组略有不同的项目。第一组方案用奇异摄动方法处理各种几何构造。这些包括使用交叉极小曲面，极小超曲面和高维欧氏空间中的常平均曲率超曲面以及爱因斯坦四维流形的去奇异化的构造。第二组项目位于广义相对论领域。特别是，PI与Christodoulou合作，将试图解决Kerr和Schwarzschild黑洞的唯一性和稳定性问题。 极小曲面是由各种物理曲面产生的，它们具有使所有由同一空间轮廓限定的曲面的表面积最小化的显著性质。极小曲面也可以用来模拟凝聚态物质。黑洞的稳定性问题，涉及检查黑洞与弱引力波的相互作用，在宇宙学中有重要的应用。