Topics in black holes and string theory

Part I. Investigations of the Matrix Model Proposal for M-theory. The Matrix Model is a proposed formulation of M-theory, which in turn is the fundamental eleven-dimensional theory underlying string theory. In the first chapter, we review the evidence for the Matrix Model proposal. In the second chapter, we analyze compactifications of the Matrix Model and the relation to compactified M-theory. We find that this correspondence provides many new results about the strong coupling behaviour of supersymmetric Yang-Mills theories. We discuss the results obtained for maximally supersymmetric Yang-Mills theory in dimensions 1 through 6. We find novel features like the opening up of new dimensions in the limit of strong coupling.; In the next chapter, we consider a more complicated compactification of the matrix model on an ALE space, in which the background is not toroidal. We show that the features of the matrix model are in agreement with string theory on the ALE space, thus providing further evidence for the matrix model proposal.; We then compare amplitudes in supergravity with the predictions of the matrix model. We discuss a particular amplitude involving three gravitons in supergravity. The leading-order result is in disagreement, but we show that it is plausible that higher order corrections will bring the two results into agreement.; Part II. Hawking Radiation from Black Holes and D-branes. D-branes are solitonic objects in string theory which have been used to model black holes. In this part of the thesis, we perform detailed comparison of Hawking radiation from black holes with the corresponding prediction from the D-brane model. We perform the analysis for two types of scalars. We show that the absorption rates for minimal scalars are in agreeement with the D-brane analysis. The absorption rates for the other type of scalar--which we call "intermediate" scalars--are more difficult to compute, and we can only compute them for particular ranges of the parameters. However, in all these ranges, we find agreement with the D-brane prediction.