To determine boundedness or otherwise of Scattering maps in gravitational collapse spacetimes.

确定引力塌缩时空中散射图的有界性或其他方面。

• 批准号: 1936235
• 金额: --
• 依托单位: University of Cambridge
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2017
• 资助国家: 英国
• 起止时间: 2017 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-1936235
• 关键词: determine; boundedness; otherwise; Scattering; maps

This thesis will concern study of various mathematical problems in general relativity, including questions on the longtime behaviour of the Einstein equations, the properties of black hole spacetimes and the structure of singularities. It will be mainly focusing on scattering maps of the wave equation in the case of gravitational collapse, such as the Oppenheimer-Snyder spacetime. It will address the case of whether these maps and their inverses are bounded, by using energy currents and conformal methods. These maps have not been rigorously studied previously, and yet are used in work surrounding Hawking radiation frequently.

这篇论文将研究广义相对论中的各种数学问题，包括爱因斯坦方程的长期行为、黑洞时空的性质和奇点的结构。它将主要集中在引力坍缩情况下波动方程的散射图，例如奥本海默-斯奈德时空。它将通过使用能量流和保角方法来解决这些映射及其逆是否有界的情况。这些地图以前没有经过严格的研究，但经常被用于围绕霍金辐射的工作。

项目成果

The Scattering Map on Collapsing Charged Spherically Symmetric Spacetimes

塌缩带电球对称时空的散射图

• DOI: 10.48550/arxiv.2309.03025
• 发表时间: 2023
• 作者: Alford F

A Mathematical Study of Hawking Radiation on Collapsing, Spherically Symmetric Spacetimes

坍缩球对称时空中霍金辐射的数学研究

• DOI: 10.17863/cam.82459
• 发表时间: 2021
• 作者: Alford F

The Scattering Map on Oppenheimer-Snyder Space-Time

奥本海默-斯奈德时空散射图

• DOI: 10.1007/s00023-020-00905-5
• 发表时间: 2020
• 期刊: Annales Henri Poincaré
• 作者: Alford F