To refer to this page use: http://arks.princeton.edu/ark:/88435/pr1t942
 Abstract: We revisit the extension problem for Killing vector-fields in smooth Ricci flat manifolds, and its relevance to the black hole rigidity problem. We prove both a stronger version of the main local extension result established earlier, as well as two types of results concerning non-extendibility. In particular, we show that one can find local, stationary, vacuum extensions of a Kerr solution $\mathcal {K}(m,a)$, \$ 0