Where do moving punctures go?

TL;DR

This paper investigates the behavior of moving puncture methods in black-hole binary simulations, revealing that slices evolve to a stationary state forming a finite-radius cylinder, and introduces time-independent puncture-like data.

Contribution

It provides new insights into the geometric structure of slices in moving puncture evolutions and presents time-independent puncture data for Schwarzschild spacetime.

Findings

Slices evolve to a stationary cylinder of finite Schwarzschild radius

Puncture slices lose contact with the second asymptotic end

Introduction of time-independent puncture-like data

Abstract

Currently the most popular method to evolve black-hole binaries is the ``moving puncture'' method. It has recently been shown that when puncture initial data for a Schwarzschild black hole are evolved using this method, the numerical slices quickly lose contact with the second asymptotically flat end, and end instead on a cylinder of finite Schwarzschild coordinate radius. These slices are stationary, meaning that their geometry does not evolve further. We will describe these results in the context of maximal slices, and present time-independent puncture-like data for the Schwarzschild spacetime.