Overview

General relativity came to life in 1915, when Albert Einstein formulated his field equations. These unify space, time, and gravitation, where the latter acts through curvature. Thereby the laws of physics obtain a geometric nature. Mathematical general relativity investigates spacetimes, which are manifolds equipped with a Lorentzian metric obeying the related Einstein-matter systems of nonlinear partial differential equations. The fruitful interactions of mathematics and physics in general relativity have produced breakthroughs in all the related research fields. This volume includes 14 articles presenting aspects of the most important general relativity research of the past 100 years. Among them we find cosmological and non-cosmological questions, the Cauchy problem for the Einstein equations, stability results, black holes and their formation, gravitational waves and their memory effect, the concept of energy, and the asymptotics of spacetimes. Through geometric analysis and advanced theory of nonlinear partial differential equations, long-standing problems have been solved lately that had remained locked since the beginnings of this beautiful theory of general relativity. Many more burning questions have been formulated and are yet to be answered.

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9781571463081

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Lydia Bieri, University of Michigan, USA Shing-Tung Yau, Harvard University, USA

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