Accurate black hole evolutions by fourth-order numerical relativity

TL;DR

This paper introduces a new fourth-order numerical relativity framework for simulating binary black holes, achieving higher accuracy in gravitational waveform predictions compared to traditional second-order methods.

Contribution

It develops a versatile, high-order finite differencing approach for Einstein's equations, validated through standard tests and applied to binary black hole collisions with improved waveform accuracy.

Findings

Demonstrated fourth-order convergence in test problems

Achieved more accurate gravitational waveforms

Significant improvements over second-order methods

Abstract

We present techniques for successfully performing numerical relativity simulations of binary black holes with fourth-order accuracy. Our simulations are based on a new coding framework which currently supports higher order finite differencing for the BSSN formulation of Einstein's equations, but which is designed to be readily applicable to a broad class of formulations. We apply our techniques to a standard set of numerical relativity test problems, demonstrating the fourth-order accuracy of the solutions. Finally we apply our approach to binary black hole head-on collisions, calculating the waveforms of gravitational radiation generated and demonstrating significant improvements in waveform accuracy over second-order methods with typically achievable numerical resolution.