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

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。

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.