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For any vacuum initial data set, we define a local, non-negative scalarquantity which vanishes at every point of the data hypersurface if and only ifthe data are {\em Kerr initial} data. Our scalar quantity only depends on thequantities used to construct the vacuum initial data set which are theRiemannian metric defined on the initial data hypersurface and a symmetrictensor which plays the role of the second fundamental form of the embeddedinitial data hypersurface. The dependency is {\em algorithmic} in the sensethat given the initial data one can compute the scalar quantity by algebraicand differential manipulations, being thus suitable for an implementation in anumerical code. The scalar could also be useful in studies of the non-linearstability of the Kerr solution because it serves to measure the deviation of avacuum initial data set from the Kerr initial data in a local and algorithmicway.

A local non-negative initial data scalar characterisation of the Kerr solution