Cook’s boundary condition on the conformal factor y (Equation (82) in [72Jump To The Next Citation Point]) is equivalent to Q(l) = 0 which (in the co-rotating case, or more generally, when the 2-metric on S is axi-symmetric) reduces to Lty = 0 on S. The Yo et al. boundary condition on y (Equation (48) of [190]) is equivalent to Lty = 0 on S, where, however, the evolution vector field ta is obtained by a superposition of two Kerr-Schild data.