Solving the Hamiltonian constraint for 1+log trumpets

TL;DR

This paper introduces a new numerical method for solving the Hamiltonian constraint in black hole initial data, specifically addressing the challenges posed by trumpet puncture geometries, and demonstrates its effectiveness in binary black hole simulations.

Contribution

The authors develop a novel approach using inverse powers of the conformal factor to solve the Hamiltonian constraint for trumpet punctures, extending the puncture method.

Findings

Reduced initial gauge dynamics in binary black hole evolutions

Successful numerical examples for single and binary trumpet punctures

Enhanced treatment of coordinate singularities in puncture data

Abstract

The puncture method specifies black hole data on a hypersurface with the aid of a conformal rescaling of the metric that exhibits a coordinate singularity at the puncture point. When constructing puncture initial data by solving the Hamiltonian constraint for the conformal factor, the coordinate singularity requires special attention. The standard way to treat the pole singularity occurring in wormhole puncture data is not generally applicable to trumpet puncture data. We investigate a new approach based on inverse powers of the conformal factor and present numerical examples for single punctures of the wormhole and 1+log-trumpet type. Additionally, we describe a method to solve the Hamiltonian constraint for two 1+log trumpets for a given extrinsic curvature with non-vanishing trace. We investigate properties of this constructed initial data during binary black hole evolutions and find that the initial gauge dynamics is reduced.