Trumpet-puncture initial data for black holes

TL;DR

This paper introduces a new, easy-to-implement puncture method for constructing initial data of black holes in trumpet geometry, applicable to boosted and binary black holes, with potential extensions to spinning black holes.

Contribution

It presents a novel puncture-based approach for black hole initial data in trumpet geometry that simplifies numerical implementation and avoids internal boundary conditions for non-spinning cases.

Findings

Numerical results for boosted black holes demonstrate the method's effectiveness.

Binary black hole initial data can be generated using this approach.

Potential for extending the method to spinning black holes is discussed.

Abstract

We propose a new approach, based on the puncture method, to construct black hole initial data in the so-called trumpet geometry, i.e. on slices that asymptote to a limiting surface of non-zero areal radius. Our approach is easy to implement numerically and, at least for non-spinning black holes, does not require any internal boundary conditions. We present numerical results, obtained with a uniform-grid finite-difference code, for boosted black holes and binary black holes. We also comment on generalizations of this method for spinning black holes.