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

Understand

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.