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

TL;DR

This paper investigates whether asymptotically flat initial data for black holes can be constructed using evolutionary forms of the Einstein constraints, demonstrating successful numerical methods for near-Kerr configurations.

Contribution

It introduces methods to generate asymptotically flat initial data using parabolic-hyperbolic and algebraic-hyperbolic constraint forms, verified through numerical integration.

Findings

Successfully constructed asymptotically flat initial datasets

Controlled falloff rates by manipulating monopole parts of variables

Validated methods through numerical integration of near-Kerr configurations

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.