On complete stationary vacuum initial data

We describe a proof of M.T. Anderson’s result (Anderson, 2000) on the rigidity of complete stationary initial data for the Einstein vacuum equations in spacetime dimension 3+13+1, under an extra assumption on the norm of the stationary Killing vector field. The argument only involves basic comparison geometry along with some Bochner–Weitzenböck formula techniques. We also discuss on the possibility to extend these techniques to higher dimensions.