The "non-Kerrness" of domains of outer communication of black holes and exteriors of stars

T. Bäckdahl, J. A. Valiente Kroon

In this article we construct a geometric invariant for initial data sets for the vacuum Einstein field equations $(\mathcal{S},h_{ab},K_{ab})$, such that $\mathcal{S}$ is a 3-dimen…