From GLC to double-null coordinates and illustration with static black holes

TL;DR

This paper introduces a coordinate system derived from GLC coordinates that is equivalent to double-null coordinates, providing useful tools for cosmology and black hole physics, with applications to static black holes and particle trajectories.

Contribution

It establishes a new coordinate system based on GLC coordinates that is equivalent to double-null coordinates, with applications to static black holes and astrophysics.

Findings

Coordinates simplify descriptions of black hole metrics.

They facilitate analysis of particle and photon trajectories.

Brief insights into ultra-relativistic particle flight times.

Abstract

We present a system of coordinates deriving directly from the so-called Geodesic Light-Cone (GLC) coordinates and made of two null scalars intersecting on a 2-dimensional sphere parameterized by two constant angles along geodesics. These coordinates are shown to be equivalent to the well-known double-null coordinates. As GLC, they present interesting properties for cosmology and astrophysics. We discuss this latter topic for static black holes, showing simple descriptions for the metric or particles and photons trajectories. We also briefly comment on the time of flight of ultra-relativistic particles.