MG15 - Talk detail

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In their famous 1938 Annals of Mathematics paper: `The Gravitational Equations and the Problem of Motion,' Einstein, Infeld, and Hoffmann claimed that the field equations of general relativity theory alone determine the equations of motion of matter particles, viewed as naked point-singularities in space-like slices of spacetime. Their claim was generalized to charged naked point-singularities by Infeld's student Wallace in 1941. Although non-rigorous and full of questionable assumptions, these works have become the template of many follow-up studies, in particular the computation of gravitational wave signals and their feedback on the motion of the sources. This talk surveys our rigorous understanding of the classical joint initial value problem for N point-charges and their electromagnetic fields in special and general relativity. The presentation includes a special-relativistic local well-posedness theorem, proved jointly with A. Shadi Tahvildar-Zadeh, which uses an electromagnetic vacuum law that avoids the infinity problems of the Maxwell-Lorentz field equations. It also outlines an ongoing joint project with A. S. T.-Z. and Annegret Burtscher, in which a well-defined general relativistic formulation of the problem is laid out, one that still awaits rigorous treatment.

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