Numerical Calculation of Conformally Smooth Hyperboloidal Data

TL;DR

This paper presents a numerical scheme for generating conformally smooth hyperboloidal initial data for Einstein's equations, applicable to various spacetime topologies including asymptotically Minkowski and Schwarzschild.

Contribution

It introduces a method to compute three-dimensional conformal data from free functions, accommodating different topologies and null infinity configurations.

Findings

Successfully computes data for spacetimes with one spherical null infinity

Extends to data with two toroidal null infinities

Outlines modifications for multiple black hole spacetimes

Abstract

This is the third paper in a series describing a numerical implementation of the conformal Einstein equation. This paper describes a scheme to calculate (three) dimensional data for the conformal field equations from a set of free functions. The actual implementation depends on the topology of the spacetime. We discuss the implementation and exemplary calculations for data leading to spacetimes with one spherical null infinity (asymptotically Minkowski) and for data leading to spacetimes with two toroidal null infinities (asymptotically A3). We also outline the (technical) modifications of the implementation needed to calculate data for spacetimes with two and more spherical null infinities (asymptotically Schwarzschild and asymptotically multiple black holes).