Bowen-York trumpet data and black-hole simulations

TL;DR

This paper develops a method to construct initial data for black-hole simulations in trumpet form, improving the accuracy and efficiency of numerical relativity simulations involving black holes.

Contribution

It extends the puncture method to create Bowen-York trumpet data, providing existence and uniqueness proofs, and demonstrates advantages in black-hole mass prescription.

Findings

Constructed Bowen-York trumpet initial data using a pseudospectral solver.

Evolved binary data and compared with standard wormhole data.

Showed black-hole mass can be prescribed a priori for boosted trumpets.

Abstract

The most popular method to construct initial data for black-hole-binary simulations is the puncture method, in which compactified wormholes are given linear and angular momentum via the Bowen-York extrinsic curvature. When these data are evolved, they quickly approach a ``trumpet'' topology, suggesting that it would be preferable to use data that are in trumpet form from the outset. To achieve this, we extend the puncture method to allow the construction of Bowen-York trumpets, including an outline of an existence and uniqueness proof of the solutions. We construct boosted, spinning and binary Bowen-York puncture trumpets using a single-domain pseudospectral elliptic solver, and evolve the binary data and compare with standard wormhole-data results. We also show that for boosted trumpets the black-hole mass can be prescribed {\it a priori}, without recourse to the iterative procedure that is necessary for wormhole data.