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Title:
Relating relativistic point sources to continuous matter distributions
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Abstract:
Due to linearity of the Poisson equation one can describe a Newtonian gravitational point source as a limit of continuous matter distributions, and vice versa: one can view a continuous matter distribution as a limit of a sequence of point source configurations. In general relativity this idea is much more difficult to implement because the Einstein equations are non-linear. In this talk we present a mathematically rigorous way of executing these ideas at the level of time-symmetric initial data. The key is to pay special attention to (self-)interaction energies of point sources and to use intrinsic flat limit developed by Sormani and Wenger. This work is a collaboration with Noah Benjamin and Tatyana Benko.
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