Covariant Radiative Transfer for Black Hole Spacetimes

TL;DR

This paper develops covariant forms of the radiative transfer equation suitable for numerical simulations of relativistic radiation flows around black holes, covering both flat and curved spacetimes.

Contribution

It provides explicit covariant radiative transfer equations in spherical-polar coordinates for Minkowski and Kerr spacetimes, building on previous foundational work.

Findings

Derived covariant radiative transfer equations for curved spacetime.

Formulated equations explicitly in spherical-polar coordinates.

Applicable to numerical simulations of relativistic astrophysical flows.

Abstract

It has now become possible to study directly, via numerical simulation, the evolution of relativistic, radiation-dominated flows around compact objects. With this in mind we set out explicitly covariant forms of the radiative transfer equation that are suitable for numerical integration in curved spacetime or flat spacetime in curvilinear coordinates. Our work builds on and summarizes in consistent form earlier work by Lindquist, Thorne, Morita and Kaneko, and others. We give explicitly the basic equations in spherical-polar coordinates for Minkowski space and the Kerr spacetime in Kerr-Schild coordinates.