# Construction of high precision numerical single and binary black hole initial data

## TL;DR

This paper introduces a new implicit numerical method for constructing initial data of single and binary black holes in general relativity, offering stability and boundary condition advantages.

## Contribution

It presents a novel implicit solver for the parabolic-hyperbolic constraints, improving stability and boundary condition handling in black hole initial data construction.

## Key findings

- The method is unconditionally stable.
- It does not require boundary conditions in strong fields.
- Successfully tested against exact solutions.

## Abstract

We present a novel implicit numerical implementation of the parabolic-hyperbolic formulation of the constraints of general relativity. The proposed method is unconditionally stable, has the advantage of not requiring the imposition of any boundary conditions in the strong field regime, and offers a holistic (all inclusive) approach to the construction of single and binary black hole initial data. The new implicit solver is extensively tested against known exact black hole solutions and is used to construct initial data for several single and binary black hole configurations.