Relativistic radiation hydrodynamics in a reference-metric formulation

TL;DR

This paper introduces a new formulation of relativistic radiation hydrodynamics using a reference-metric approach, enabling better numerical simulations in curved spacetimes, demonstrated through tests including shock solutions and black hole collapse.

Contribution

It presents a novel reference-metric formalism for relativistic radiation hydrodynamics suitable for curvilinear coordinates, with validation through numerical tests.

Findings

Accurate modeling of shocks in flat spacetime.

Successful simulation of black hole formation from collapse.

Effective transition from transient to diffusion phases in collapse.

Abstract

We adopt a two-moment formalism, together with a reference-metric approach, to express the equations of relativistic radiation hydrodynamics in a form that is well-suited for numerical implementations in curvilinear coordinates. We illustrate the approach by employing a gray opacity in an optically thick medium. As numerical demonstrations we present results for two test problems, namely stationary, slab-symmetric solutions in flat spacetimes, including shocks, and heated Oppenheimer-Snyder collapse to a black hole. For the latter, we carefully analyze the transition from an initial transient to a post-transient phase that is well described by an analytically-known diffusion solution. We discuss the properties of the numerical solution when rendered in moving-puncture coordinates.