Inspired by the example of Abdelqader and Lake for the Kerr metric, we construct local scalar polynomial curvature invariants that vanish on the horizon of any stationary black hole: the squared norms of the wedge products of $n$ linearly independent gradients of scalar polynomial curvature invariants, where $n$ is the local cohomogeneity of the spacetime.

• Received 21 January 2015

DOI:https://doi.org/10.1103/PhysRevLett.114.141102