# Relativistic sonic geometry for isothermal accretion in the Kerr metric

## TL;DR

This paper explores how relativistic acoustic spacetime structures emerge in isothermal accretion flows onto Kerr black holes, revealing effects of black hole spin on acoustic horizons and stability.

## Contribution

It introduces a unified approach to derive the acoustic metric from different perturbation quantities in Kerr accretion flows, highlighting the influence of black hole spin.

## Key findings

- Acoustic black holes form at transonic points of the flow.
- Acoustic white holes appear at shock locations.
- The acoustic surface gravity depends on accretion variables and black hole spin.

## Abstract

We linearly perturb advective isothermal transonic accretion onto rotating astrophysical black holes to study the emergence of the relativistic acoustic spacetime and to investigate how the salient features of such spacetime get influenced by the spin angular momentum of the black hole. We have perturbed three different quantities - the velocity potential, the mass accretion rate and the relativistic Bernoulli's constant to show that the acoustic metric obtained for these three cases are same up to a conformal factor. By constructing the required causal structures, it has been demonstrated that the acoustic black holes are formed at the transonic points of the flow and acoustic white holes are formed at the shock location. The corresponding acoustic surface gravity has been computed in terms of the relevant accretion variables and the background metric elements. The linear stability analysis of the background stationary flow has been performed.