Testing excision techniques for dynamical 3D black hole evolutions

TL;DR

This paper compares excision and non-excision methods in 3D black hole simulations, demonstrating that excision accurately preserves waveforms and stability, validating its use in numerical relativity.

Contribution

It provides a numerical validation of excision techniques in 3D black hole evolutions through comparative simulations of distorted and binary black holes.

Findings

Excision yields stable, long-term evolutions similar to full grid methods.

Waveforms from excision and non-excision simulations converge.

Excision effectively isolates the black hole interior, enabling accurate exterior evolution.

Abstract

We perform both distorted black hole evolutions and binary black hole head on collisions and compare the results of using a full grid to results obtained by excising the black hole interiors. In both cases the evolutions are found to run essentially indefinitely, and produce the same, convergent waveforms. Further, since both the distorted black holes and the head-on collision of puncture initial data can be carried out without excision, they provide an excellent dynamical test-bed for excision codes. This provides a strong numerical demonstration of the validity of the excision idea, namely the event horizon can be made to "protect" the spacetime from the excision boundary and allow an accurate exterior evolution.