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

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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.