Note on ingoing coordinates for binary black holes

TL;DR

This paper introduces an ingoing coordinate transformation for binary black hole metrics, enabling numerical simulations to include regions inside the horizons, which was not possible with previous coordinate systems.

Contribution

The paper develops a new ingoing coordinate system that extends previous corotating coordinates through black hole horizons into their interiors.

Findings

Coordinate transformation extends metric inside horizons

Enables initial data for numerical simulations

Facilitates more accurate black hole modeling

Abstract

In a previous paper, a binary black hole four-metric was presented in a post-Newtonian corotating coordinate system valid only up to the holes' apparent horizons. In this paper, I define an ingoing coordinate transformation that extends this corotating coordinate system through the holes' horizons and into their interiors. The motivation for using ingoing coordinates is that numerical simulations of black holes require the computational grid to extend inside the horizons. The coordinate transformation presented here makes the binary black hole four-metric suitable as a source of initial data for numerical simulations.