Acoustic geometry through perturbation of mass accretion rate - radial flow in static spacetimes

TL;DR

This paper derives the relativistic acoustic geometry from perturbations of mass accretion rate in static spacetimes, showing stability of accretion and similarities to non-relativistic cases, with applications to Schwarzschild and Rindler spacetimes.

Contribution

It introduces a novel relativistic derivation of acoustic geometry via mass accretion rate perturbations, extending previous non-relativistic analyses.

Findings

The causal structure of the relativistic acoustic geometry is similar to that from velocity potential perturbations.

The accretion process is demonstrated to be stable under perturbations.

Explicit examples in Schwarzschild and Rindler spacetimes are discussed.

Abstract

In this work we present an alternative derivation of the general relativistic acoustic analogue geometry by perturbing the mass accretion rate or flux of an ideal fluid flowing radially in a general static and spherically symmetric spacetime. To the best of our knowledge, this has so far been done in non-relativistic scenario. The resulting causal structure of the two dimensional acoustic geometry is qualitatively similar to that one derives via the perturbation of the velocity potential. Using this, we then briefly discuss the stability issues by studying the wave configurations generated by the perturbation of the mass accretion rate, and formally demonstrate the stability of the accretion process. This is in qualitative agreement with earlier results on stability, established via study of wave configurations generated by the perturbation of velocity potential, by using the acoustic geometry associated with it. We further discuss explicit examples of the Schwarzschild and Rindler spacetimes.