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.

9704338 Kapouleas该提案由两个有点不同的项目组成。第一组项目通过奇异的渗透方法处理了各种几何构造。这些包括使用相交最小表面，最小的超曲面和恒定的平均曲率超曲面的构造，在较高的欧几里得空间中，以及爱因斯坦的四个manifolds。第二组项目位于一般相对论领域。特别是，PI与Christodoulou合作，将尝试为Kerr和Schwarzschild黑洞解决独特性和稳定问题。 最小表面作为各种物理表面出现。它们具有极大的特性，可以最大程度地减少所有表面之间的表面积，并以相同的空间轮廓界定。最小表面也可以用于建模凝结物。黑洞的稳定性问题涉及检查黑洞与弱重力波的相互作用，在宇宙学中具有重要的应用。