# Asymptotics of solutions of a hyperbolic formulation of the constraint equations

## TL;DR

This paper investigates the asymptotic behavior of solutions to a hyperbolic formulation of Einstein's constraint equations, using numerical methods to analyze perturbations of Schwarzschild data and their asymptotic properties.

## Contribution

It introduces a numerical approach to study the asymptotics of hyperbolic constraint solutions and highlights potential issues with asymptotic conditions in generic initial data.

## Key findings

- Most generic initial data may violate fundamental asymptotic conditions
- Numerical construction of perturbations of Schwarzschild data
- Potential need to exploit free data to ensure proper asymptotics

## Abstract

In this paper we consider the hyperbolic formulation of the constraints introduced by R\'acz. Using the numerical framework recently developed by us we construct initial data sets which can be interpreted as nonlinear perturbations of Schwarzschild data in Kerr-Schild coordinates and investigate their asymptotics. Our results suggest that, unless one finds a way to exploit the freedom to pick the free part of the initial data in some suitable way, generic initial data sets obtained by this method may violate fundamental asymptotic conditions.