Is the flip-flop behaviour of accretion shock cones on to black holes an effect of coordinates?

TL;DR

This study investigates whether the observed flip-flop behavior of accretion shock cones onto black holes is an artifact of coordinate choice by comparing Kerr-Schild and Boyer-Lindquist coordinates in relativistic simulations.

Contribution

It demonstrates that flip-flop oscillations occur in Boyer-Lindquist coordinates but are absent in Kerr-Schild coordinates, suggesting coordinate effects influence the observed shock cone behavior.

Findings

Flip-flop behavior appears only in Boyer-Lindquist coordinates.

Kerr-Schild coordinates show oscillations that diminish with resolution.

Coordinate choice affects the observed shock cone dynamics.

Abstract

We study numerically the relativistic Bondi-Hoyle accretion of an ideal gas onto a Kerr fixed background space-time on the equatorial plane with s-lab symmetry. We use both Kerr-Schild (KS) and Boyer-Lindquist (BL) coordinates. We particularly focus on the study of the flip-flop motion of the shock cone formed when the gas is injected at supersonic speed. The development of the flip-flop instability of the shock cone in the relativistic regime was reported recently for the first time. We reproduce the flip-flop behaviour found in the past when BL coordinates are used, and perform similar numerical experiments using horizon penetrating KS coordinates. We find that when using KS coordinates the shock cone oscillates, however such oscillations are not of the flip-flop type and their amplitude decrease with resolution.