Analytical Representation of a Black Hole Puncture Solution

TL;DR

This paper presents an analytical solution for a black hole puncture, enhancing the tools available for testing and calibrating numerical relativity codes that simulate black hole spacetimes.

Contribution

It provides an analytical construction of the black hole puncture solution, previously known only numerically, improving its utility for code testing.

Findings

Analytical solution matches numerical results

Simplifies testing of numerical relativity codes

Enhances understanding of black hole puncture evolution

Abstract

The ``moving puncture'' technique has led to dramatic advancements in the numerical simulations of binary black holes. Hannam et.al. have recently demonstrated that, for suitable gauge conditions commonly employed in moving puncture simulations, the evolution of a single black hole leads to a well-known time-independent, maximal slicing of Schwarzschild. They construct the corresponding solution in isotropic coordinates numerically and demonstrate its usefulness, for example for testing and calibrating numerical codes that employ moving puncture techniques. In this Brief Report we point out that this solution can also be constructed analytically, making it even more useful as a test case for numerical codes.