Tidal shapes and shifts on rotating black holes

The shape of the tide raised on a rotating black hole by an exterior perturbation is investigated. An expression is given for the perturbed curvature of the two-surface formed by the intersection of the event horizon and a surface of constant time. The result involves only the perturbation in the Weyl tensor component Ψ₀ which solves the Teukolsky equation. An application is made to the tide raised by an exterior moon outside a slowly rotating black hole. In this case the position of the tidal bulge is shifted away from the position of the moon in a way analogous to the lag of the tide in the earth-moon system.