A moving medium simulation of Schwarzschild black hole optics

TL;DR

This paper presents a fluid flow simulation modeling electromagnetic wave propagation near a Schwarzschild black hole, introducing a new coordinate system that bridges existing coordinate representations.

Contribution

It introduces a novel fluid flow simulation approach with a constant refractive index to model black hole optics and derives a new coordinate system in Gordon's form.

Findings

Derived a new coordinate system interpolating between Kerr-Schild and Painleve-Gullstrand coordinates.

Demonstrated the fluid flow simulation's ability to replicate black hole optical properties.

Connected the simulation framework with existing coordinate representations.

Abstract

An explicit fluid flow simulation of electromagnetic wave propagation in the gravitational field of a Schwarzschild black hole is given. The fluid has a constant refractive index and a spherically symmetric inward directed flow. The resulting form of the metric leads to a new coordinate system in which the Schwarzschild vacuum is written in Gordon's form. It is shown that a closely related coordinate system interpolates between the Kerr-Schild and Painleve-Gullstrand coordinates.