Cook’s boundary condition on the conformal factor (Equation (82) in [70]) is equivalent to which (in the co-rotating case, or more generally, when the 2-metric on is axi-symmetric) reduces to on . The Yo et al. boundary condition on (Equation (48) of [190]) is equivalent to on , where, however, the evolution vector field is obtained by a superposition of two Kerr–Schild data.