Wednesday, July 5, 2023
10:00 am. (sharp)
Zoom Web Conference
PhD Candidate: Eva Politou
Supervisor: Stefanos Aretakis
Thesis title: A Geometric Framework for Conservation Laws Along Null
Hypersurfaces and their Relation to Huygens’ Principle
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In the present thesis we examine two main topics. In the first part, we use the general theory of local conservation laws for arbitrary partial differential equations to provide a geometric framework for conservation laws on characteristic null hypersurfaces. The operator of interest is the wave operator on general four-dimensional Lorentzian manifolds restricted on a null hypersurface. In the second part of the thesis, we investigate relations between the geometric conditions that lead to the validity of Huygens’ principle and those that give rise to conservation laws along null hypersurfaces for the wave operator. We apply our results in spacetimes such as the Minkowski, Schwarzschild, and Reissner-Nordström, as well as in general spherically symmetric spacetimes.
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The draft of the thesis can be found here: Eva’s Thesis
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