Toward computing gravitational initial data without elliptic solvers

TL;DR

This paper compares two novel methods for generating gravitational initial data without elliptic solvers, aiming to improve black hole simulation setups by providing a unified computational framework.

Contribution

It introduces and compares algebraic-hyperbolic and parabolic-hyperbolic methods, and develops a unified code infrastructure for their implementation.

Findings

Methods successfully formulated as hyperbolic systems

Unified computational infrastructure developed

Potential application in black hole initial data setup

Abstract

Two new methods have been proposed for solving the gravitational constraints without using elliptic solvers by formulating them as either an algebraic-hyperbolic or parabolic-hyperbolic system. Here, we compare these two methods and present a unified computational infrastructure for their implementation as numerical evolution codes. An important potential application of these methods is the prescription of initial data for the simulation of black holes. This paper is meant to support progress and activity in that direction.