Is it possible to construct asymptotically flat initial data using the evolutionary forms of the constraints?

Abstract: Near-Kerr black hole initial datasets are constructed by applying either the parabolic-hyperbolic or the algebraic-hyperbolic form of the constraints. In both cases, strongly and weakly asymptotically flat initial datasets with desirable falloff rates are produced by controlling only the monopole part of one of the freely specifiable variables. The viability of the applied method is verified by numerically integrating the evolutionary forms of the constraint equations in the case of various near-Kerr configurations.