Not all spacetime coordinates for general-relativistic ray tracing are created equal

TL;DR

This paper examines how the choice of spacetime coordinates and initial conditions in general-relativistic ray tracing affects the computed images of black holes, highlighting the importance of coordinate selection for accurate simulations.

Contribution

It demonstrates that coordinate choices significantly influence ray tracing results and identifies optimal coordinates for accurate black-hole imaging in general relativity.

Findings

Coordinate choice impacts ray tracing solutions

Optimal coordinates yield consistent black-hole images

Differences are within numerical and algorithmic errors

Abstract

Models for the observational appearance of astrophysical black holes rely critically on accurate general-relativistic ray tracing and radiation transport to compute the intensity measured by a distant observer. In this paper, we illustrate how the choice of coordinates and initial conditions affect this process. In particular, we show that propagating rays from the camera to the source leads to different solutions if the spatial part of the momentum of the photon points towards the horizon or away from it. In doing this, we also show that coordinates that are well suited for numerical General-Relativistic MagnetoHydroDynamic (GRMHD) simulations are typically not optimal for generic ray tracing. We discuss the implications for black-hole images and show that radiation transport in optimal and non-optimal spacetime coordinates lead to the same images up to numerical errors and algorithmic choices.