Mathematical Challenges of General Relativity

Physics

Scientific paper

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Scientific paper

It should not come as a surprise that General Relativity, the most mathematical of all our physical theories, presents an extremely fertile ground for mathematicians. From its inception General Relativity has attracted the attention of geometers and analysts; yet, due to its manifold difficulties, it has failed to produce that constant stream of results needed to establish it as a well defined field of Mathematics. This, I believe, has been or is about to be changed in recent years due to a host of new and deep results obtained by sophisticated mathematical techniques. In my lecture I plan to talk mainly about some of the recent developments in connection with the problem of evolution and discuss some of the most promising avenues of research in this regard, but first I ought to start with a short review of the main accomplishments in the mathematical theory of General Relativity ...

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