Kerr principal null directions from Bel--Robinson and Kummer surfaces

In the Kerr geometry, we calculate various surfaces of constant curvature invariants. These extend well beyond the Kerr horizon, and we argue that they might be of observational significance in connection with non-minimally coupled matter fields. Moreover, we demonstrate that the principal null directions of the Kerr geometry can be obtained by projections involving either the Bel--Robinson or the Kummer tensor. We conjecture that this is also possible in more general settings.