In this talk I will discuss an extension of Dain's construction of geometric invariants characterising stationarity to the case of initial data sets for the Einstein equations corresponding to black hole spacetimes. We prove the existence and uniqueness of solutions to a boundary value problem showing that one can always find approximate Killing vectors in black hole spacetimes and these coincide with actual Killing vectors when they are present. Moreover, I will discuss the relation between the boundary data for the approximate Killing vector equation and the notion of stability for MOTS.
Dr. Juan A. Valiente Kroon (London): Dain's invariant for black hole initial data
