一个边界-局部质量共旋和非对称的质量超标的表现形式
1Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria.
概括
我们开发了一个新的共循环来定义一个相对的能量-动量密度为非对称地局部超标 (ALH) 变 manifolds. 这种几何不变量对于理解过度波形多样体的质量至关重要.
科学领域:
- 不同几何学微分几何学
- 数学物理 数学物理
- 几何分析 几何分析
背景情况:
- 在广义相对论和几何分析中,非对位局部过度波动 (ALH) 多元体是必不可少的.
- 了解这些变形体的几何不变数和边界性质是一个关键的挑战.
- 现有的超大波场景中的质量计算方法存在局限性.
研究的目的:
- 构建一个可循环,将ALH指标对映射到符合无限的拖拉器值微分形式.
- 定义一个局部几何量,解释为相对能量-动量密度.
- 为了导出ALH指标的绝对不变量,并将其与超标质整数联系起来.
主要方法:
- 构建一个可循环的n-多元体与非对称相关的ALH指标.
- 分析cocycle的属性,包括在diffeomorphisms下的不变性.
- 专注于符合规范的紧度指标和跨越球体边界的整合.
- 连接到杀死初始数据 (KID) 方程.
主要成果:
- 一个在符合无限度上的拖拉器值微分形式与ALH指标有正统的关联.
- 对于合适的ALH指标,导出一个局部绝对不变数c(h).
- 在球形边界上c(h) 的集成恢复已知的过度的质量积分.
- 证明不变量是局部的,在特定的不同形态下是等同的.
结论:
- 构建的可循环为研究ALH多元体提供了一个强大的工具.
- 衍生不变提供了对超标空间几何结构和质量的新见解.
- 这项工作将微分几何和数学物理学的概念联系起来,对广义相对论有影响.
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