SoSe 18: Spezialvorlesung Einführung in die allgemeine Relativitätstheorie
Ahmad Al-Afuni
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The theory of general relativity is one of the crowning achievements of modern mathematical physics having not only pushed the boundaries of the field of differential geometry, but also having found applicability in the real world, particularly in GPS technology. This course shall deal with the mathematical foundations and formulation of general relativity as well as the recently proved positive mass theorem. It shall begin with the geometry of Minkowski spacetime, which forms the basis of Einstein's special theory of relativity and adequately describes the geometry of general relativity in the small, followed by an account of Lorentzian geometry and its tensor calculus. We shall then introduce Einstein's equation and discuss exact solutions. We shall then turn our attention to modern developments, culminating in a proof of the positive mass theorem. We shall also discuss field theories unifying gravity and other forces of nature; though these have been unsuccessful from the physical point of view, they give rise to interesting geometries.
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Literatur / References:
P. G. Bergmann. Introduction to the Theory of Relativity. Dover Publications, 1976.
R. M. Wald. General Relativity, The University of Chicago Press, 1984.
E. Witten. A new proof of the positive energy theorem. Communications in Mathematical Physics. 80.3 (1981): 381-402.
R. Bartnik. The mass of an asymptotically flat manifold. Communications on pure and applied mathematics 39.5 (1986): 661-693.
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14 Class schedule
Regular appointments