Post-Newtonian expansions are expansions of solutions to the Einstein field equations coupled to matter in a parameter epsilon = v/c (near epsilon = 0) where v is a characteristic velocity scale of the gravitating matter and c is the speed of light. This problem has been studied for many years by many people and there is an extremely large number of results available in the literature. However, the overwhelming majority of results are based on formal expansions in the parameter epsilon which lack rigorous error estimates needed to ensure the validity of the expansions as an approximation. In this talk, I will describe recent rigorous results on post-Newtonian expansions for perfect fluids. I will discuss how energy estimates for symmetric hyperbolic PDEs can be used to analyze general relativistic solutions in the singular limit epsilon -> 0 and also to derive error estimates for certain expansions in epsilon near epsilon = 0. Finally, I will discuss open problems and future research directions.

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Colloquia are designed to be of interest to a general mathematical audience and to be accessible without specialist knowledge.

There will be wine and cheese afterwards.
 

Convenor: Ian Wanless - firstname.lastname@sci.monash.edu.au