Mathematical problems in general relativity

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General relativity is a theory proposed by Einstein in 1915 as a unified theory of space, time and gravitation and is fundamentally rooted in classical mechanics. Its main objective is the understanding of the evolution of gravitational physical systems such as planetary systems, multiple stars, black holes, (a cluster of) galaxies and ultimately the universe as a whole. What distinguishes general relativity from other physical theories is that "general relativity describes the evolution of systems in terms of differential equations (i.e.~physical laws) imposed directly on the space-time metric'', connecting thus geometry,