A single-domain spectral method for black hole puncture data

TL;DR

This paper introduces a spectral method for generating highly accurate initial data for single and binary black holes, enabling precise studies of their properties and interactions.

Contribution

It develops a pseudo-spectral approach in a single domain for puncture data, improving convergence and accuracy in black hole initial data calculations.

Findings

Spectral method achieves rapid convergence of the conformal factor.

Comparison of binary black hole data with test mass limit shows significant deviations.

Accurate calculation of binding energy in the test mass limit.

Abstract

We calculate puncture initial data corresponding to both single and binary black hole solutions of the constraint equations by means of a pseudo-spectral method applied in a single spatial domain. Introducing appropriate coordinates, these methods exhibit rapid convergence of the conformal factor and lead to highly accurate solutions. As an application we investigate small mass ratios of binary black holes and compare these with the corresponding test mass limit that we obtain through a semi-analytical limiting procedure. In particular, we compare the binding energy of puncture data in this limit with that of a test particle in the Schwarzschild spacetime and find that it deviates by 50% from the Schwarzschild result at the innermost stable circular orbit of Schwarzschild, if the ADM mass at each puncture is used to define the local black hole masses.