Behaviour of Waves on Higher Dimensional Black Hole Spacetimes

高维黑洞时空中波的行为

• 批准号: 1832371
• 金额: --
• 依托单位: Imperial College London
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2016
• 资助国家: 英国
• 起止时间: 2016 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-1832371
• 关键词: Behaviour; Waves; Higher; Dimensional; Black

The concept of a black hole is one of the most fascinating predictions of Einstein's Theory of General Relativity. Understanding the stability properties of theses objects from a rigorous mathematical point of view is crucial for our interpretation of both Einstein's theory and of astrophysical observations. New mathematical techniques in the study Partial Differential Equations have been developed in the past 10-15 years to address the difficult problem of stability of black holes. At the center of these developments is a mathematically robust framework to understand wave propagation on black hole spacetimes.The aims and objectives of the research project are to investigate which of these new techniques can be applied to the study of higher dimensional black hole spacetimes. (The latter exhibit more complicated spacetime geometries and are widely studied in theoretical physics, the main example being the so-called black ring.) It is known that not all of the techniques carry through directly, so new methods in PDE analysis will have to be developed by the student to prove theorems regarding the global behaviour of waves on these spacetimes. Besides applications in theoretical physics (where various instabilities are being conjectured) this will further elucidate the intricate relationship between spacetime geometry and the dispersion of waves.

黑洞的概念是爱因斯坦一般相对论理论的最迷人的预测之一。从严格的数学角度了解这些对象的稳定性特性对于我们对爱因斯坦理论和天体物理观察的解释至关重要。在过去的10 - 15年中，已经开发了研究部分微分方程中的新数学技术，以解决黑洞稳定的困难问题。这些发展的中心是一个数学上强大的框架，以了解黑洞空间上的波浪传播。研究项目的目的和目标是研究这些新技术中的哪种可以应用于较高维度的黑洞空位的研究。 （后者表现出更复杂的时空几何形状，并在理论物理学中进行了广泛的研究，主要的例子是所谓的黑环。）众所周知，并非所有直接携带的技术都可以直接携带，因此，PDE分析中必须开发出有关这些杂物的全球性行为的PDE分析中的新方法。除了在理论物理学中的应用（在各种不稳定性的情况下），这还将进一步阐明时空几何形状与波的分散之间的复杂关系。