Bondi Accretion in Trumpet Geometries

TL;DR

This paper transforms the classical Bondi accretion solution into trumpet coordinates suitable for dynamical spacetime simulations, providing a new tool for testing and calibrating numerical relativistic codes.

Contribution

The authors derive the Bondi solution in trumpet coordinates and demonstrate its numerical evolution, facilitating improved testing of relativistic simulation codes.

Findings

Bondi solution successfully transformed into trumpet coordinates.

Numerical evolution confirms regularity and usefulness of the solution.

Provides a new benchmark for numerical relativity codes.

Abstract

The Bondi solution, which describes the radial inflow of a gas onto a non-rotating black hole, provides a powerful test for numerical relativistic codes. However, the Bondi solution is usually derived in Schwarzschild coordinates, which are not well suited for dynamical spacetime evolutions. Instead, many current numerical relativistic codes adopt moving-puncture coordinates, which render black holes in trumpet geometries. Here we transform the Bondi solution into trumpet coordinates, which result in regular expressions for the fluid flow extending into the black-hole interior. We also evolve these solutions numerically and demonstrate their usefulness for testing and calibrating numerical codes.