# Numerical initial data deformation exploiting a gluing construction: I. Exterior asymptotic Schwarzschild

## TL;DR

This paper introduces a new spectral numerical method for constructing initial data in Einstein's equations by gluing binary black hole solutions to exterior Schwarzschild data without using the conformal approach.

## Contribution

It presents a novel spectral scheme inspired by exterior asymptotic gluing that constructs initial data with binary black holes attached to Schwarzschild exterior, bypassing the conformal method.

## Key findings

- Successfully constructs initial data with binary black holes and Schwarzschild exterior.
- Demonstrates the method's effectiveness through ADM mass comparisons.
- Shows the approach's potential for more general initial data configurations.

## Abstract

In this work a new numerical technique to prepare Cauchy data for the initial value problem (IVP) formulation of Einstein's field equations is presented. Directly inspired by the exterior asymptotic gluing (EAG) result of Corvino (2000) our (pseudo)-spectral scheme is demonstrated under the assumption of axisymmetry so as to fashion composite Hamiltonian constraint satisfying initial data featuring internal binary black holes (BBH) as glued to exterior Schwarzschild initial data in isotropic form. The generality of the method is illustrated in a comparison of the ADM mass of EAG initial data sets featuring internal BBHs as modelled by Brill-Lindquist and Misner data.In contrast to the recent work of Doulis and Rinne (2016), and Pook-Kolb and Giulini (2018) we do not make use of the York-Lichnerowicz conformal framework to reformulate the constraints.