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- W2126366934 abstract "On arbitrary spacetimes, we study the characteristic Cauchy problem for Dirac fields on a light-cone. We prove the existence and uniqueness of solutions in the future of the light-cone inside a geodesically convex neighbourhood of the vertex. This is done for data in $L^2$ and we give an explicit definition of the space of data on the light-cone producing a solution in $H^1$. The method is based on energy estimates following L. Hormander (J.F.A. 1990). The data for the characteristic Cauchy problem are only a half of the field, the other half is recovered from the characteristic data by integration of the constraints, consisting of the restriction of the Dirac equation to the cone. A precise analysis of the dynamics of light rays near the vertex of the cone is done in order to understand the integrability of the constraints; for this, the Geroch-Held-Penrose formalism is used." @default.
- W2126366934 created "2016-06-24" @default.
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- W2126366934 date "2009-03-03" @default.
- W2126366934 modified "2023-10-14" @default.
- W2126366934 title "The characteristic Cauchy problem for Dirac fields on curved backgrounds" @default.
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