The theory of gravitational radiation and black holes

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The thesis will concern understanding the mathematical properties of gravitational radiation in particular in relation to processes involving black holes. This is at the centre of important developments in astronomy and in the pde analysis of the Einstein equations. Important effects discovered previously in this way include the so-called Christodoulou memory effect. The thesis will study this effect in the black hole context as well as more general questions regarding the dynamics of gravitational collapse.