Linear perturbations of low angular momentum accretion flow in the Kerr metric and the corresponding emergent gravity phenomena

TL;DR

This paper develops a linear perturbation analysis for low angular momentum accretion flows onto Kerr black holes, demonstrating stability and revealing emergent relativistic acoustic geometries linked to black hole properties.

Contribution

It introduces a novel linear stability analysis for relativistic accretion flows and uncovers emergent acoustic geometries influenced by black hole spin.

Findings

Steady accretion solutions are linearly stable.

Relativistic acoustic geometries emerge from the analysis.

Causal structures link sonic points to acoustic horizons.

Abstract

For certain geometric configuration of matter falling onto a rotating black hole, we develop a novel linear perturbation analysis scheme to perform the stability analysis of stationary integral accretion solutions corresponding to the steady state low angular momentum, inviscid, barotropic, irrotational, general relativistic accretion of hydrodynamic fluid. We demonstrate that such steady states remain stable under linear perturbation, and hence the stationary solutions are reliable to probe the black hole spacetime using the accretion phenomena.We report that a relativistic acoustic geometry emerges out as the consequence of such stability analysis procedure. We study various properties of that sonic geometry in detail. We construct the causal structures to establish the one to one correspondences of the sonic points with the acoustic black hole horizons, and the shock location with an acoustic white hole horizon. The influence of the spin of the rotating black holes on the emergence of such acoustic spacetime has been discussed.