Numerical simulations with a first order BSSN formulation of Einstein's field equations

TL;DR

This paper introduces a new first order strongly hyperbolic formulation of Einstein's equations based on BSSN, with numerical implementations demonstrating its potential for high-accuracy simulations like binary black holes.

Contribution

It presents a novel first order hyperbolic BSSN formulation with constraint damping and explores its numerical implementation using finite differences and discontinuous Galerkin methods.

Findings

Successful numerical simulations of binary black holes

Demonstration of hyperbolicity and robustness of the formulation

Potential for high-accuracy Einstein's equations simulations

Abstract

We present a new fully first order strongly hyperbolic representation of the BSSN formulation of Einstein's equations with optional constraint damping terms. We describe the characteristic fields of the system, discuss its hyperbolicity properties, and present two numerical implementations and simulations: one using finite differences, adaptive mesh refinement and in particular binary black holes, and another one using the discontinuous Galerkin method in spherical symmetry. The results of this paper constitute a first step in an effort to combine the robustness of BSSN evolutions with very high accuracy numerical techniques, such as spectral collocation multi-domain or discontinuous Galerkin methods.