Numerical evolution of multiple black holes with accurate initial data

TL;DR

This paper demonstrates the numerical evolution of three black holes using high-order initial data and compares different computational codes, highlighting the impact of initial data choices on dynamics and waveforms.

Contribution

It introduces high-order multigrid elliptic solver for initial data and compares evolutions with different codes, showing improved accuracy and insights into black hole interactions.

Findings

Sixth-order waveform convergence achieved.

Differences in dynamics due to initial data approximation.

Successful evolution of four black holes and waveform analysis.

Abstract

We present numerical evolutions of three equal-mass black holes using the moving puncture approach. We calculate puncture initial data for three black holes solving the constraint equations by means of a high-order multigrid elliptic solver. Using these initial data, we show the results for three black hole evolutions with sixth-order waveform convergence. We compare results obtained with the BAM and AMSS-NCKU codes with previous results. The approximate analytic solution to the Hamiltonian constraint used in previous simulations of three black holes leads to different dynamics and waveforms. We present some numerical experiments showing the evolution of four black holes and the resulting gravitational waveform.