Trumpet Initial Data for Boosted Black Holes

TL;DR

This paper introduces a new method for constructing initial data for boosted black holes in numerical relativity, significantly reducing junk radiation and improving the initial geometry for simulations.

Contribution

The authors present a procedure to generate initial trumpet geometry for boosted black holes, enhancing simulation accuracy and reducing initial transient radiation.

Findings

Initial data closely matches stationary trumpet geometry.

Junk radiation is reduced by up to two orders of magnitude.

Method allows for precise Lorentz boosts and superposition of multiple black holes.

Abstract

We describe a procedure for constructing initial data for boosted black holes in the moving-punctures approach to numerical relativity that endows the initial time slice from the outset with trumpet geometry within the black hole interiors. We then demonstrate the procedure in numerical simulations using an evolution code from the Einstein Toolkit that employs 1+log slicing. The Lorentz boost of a single black hole can be precisely specified and multiple, widely separated black holes can be treated approximately by superposition of single hole data. There is room within the scheme for later improvement to re-solve (iterate) the constraint equations in the multiple black hole case. The approach is shown to yield an initial trumpet slice for one black hole that is close to, and rapidly settles to, a stationary trumpet geometry. Initial data in this new approach is shown to contain initial transient (or "junk") radiation that is suppressed by as much as two orders of magnitude relative to that in comparable Bowen-York initial data.