Spectral theory of non-symmetric operators in time-dependent external fields and in globally hyperbolic spacetimes

瞬态外场和全局双曲时空中非对称算子的谱论

• 批准号: 233673047
• 负责人: Dr. Moritz Reintjes, Ph.D.
• 金额: --
• 依托单位: Arbeitsgruppe Analysis/Mathematik in den Naturwissenschaften
• 依托单位国家: 德国
• 项目类别: Research Fellowships
• 财政年份: 2013
• 资助国家: 德国
• 起止时间: 2012-12-31 至 2013-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/233673047?language=en
• 关键词: Spectral; theory; non; symmetric; operators

For the proposed research project, we plan to analyze non-symmetric operators defined on the space of solutions of the Dirac equation containing a time-dependent gravitational field. In more detail, we consider the Dirac equation defined on a globally hyperbolic spacetime background. The goal of this project is to develop a method for introducing a specific class of spectral projectors non-perturbatively, which have only been defined through a formal perturbation-expansion so far. In the case of a static spacetime those spectral projectors are supposed to be the well-known projectors on the negative (or positive) spectral subspaces of the relativistic hamilton operator. In order to develop this method step by step, we analyze the case of a closed Friedmann-Robertson-Walker (FRW) spacetime first.

在本研究项目中，我们计划分析在包含时相关引力场的狄拉克方程解空间上定义的非对称算子。更详细地说，我们考虑在全局双曲时空背景上定义的狄拉克方程。这个项目的目标是开发一种方法来引入一类特定的非摄动光谱投影仪，到目前为止，这些投影仪只能通过正式的摄动展开来定义。在静态时空的情况下，这些谱投影应该是相对论性汉密尔顿算子负（或正）谱子空间上众所周知的投影。为了逐步发展这种方法，我们首先分析了一个封闭的弗里德曼-罗伯逊-沃克（FRW）时空的情况。

项目成果

No regularity singularities exist at points of general relativistic shock wave interaction between shocks from different characteristic families

来自不同特征族的激波之间的广义相对论激波相互作用点不存在规律奇点

• DOI: 10.1098/rspa.2014.0834
• 期刊: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
• 作者: M. Reintjes;B. Temple
• 通讯作者: B. Temple