Dain's invariant on non-time symmetric initial data sets

Details

Written by Jarrod Williams

The question of stability of certain special solutions is one of the central concerns of mathematical Relativity.
In such problems, it would be useful to have a way of quantifying, in a coordinate-invariant manner, the extent to which a given initial data set deviates from a stationary regime. One approach, proposed by S. Dain,
is based on the notion of an approximate Killing vector, constructed as a solution to a fourth-order elliptic system arising from the Killing Initial Data equations. The approximate Killing vector, which was shown to exist for time symmetric initial data, may then be used to define an invariant which characterises stationarity. In this talk I will present recent work extending Dain's result to the case of non-time symmetric asymptotically Euclidean initial data, concluding with a discussion of some applications.