Emergent acoustic causality and stability analysis for axisymmetric flows through perturbation of mass accretion rate

In this work we analyse the profile of the linear perturbation of the mass accretion rate for an ideal irrotational fluid in a general static and spherically symmetric spacetime. We consider low angular momentum axisymmetric accretion flows for three different accretion disk models and make the perturbation time dependent while leaving it independent of the azimuthal angle. We show that the propagation of such perturbation can be associated with symmetric two dimensional matrices for all the three disk models, which have qualitatively similar acoustic causal properties as one derives via the perturbation of the velocity potential. Using these matrices, we next study the wave configurations generated by the perturbation of the mass accretion rate and address the stability of the accretion process. Based on this general formalism we then briefly discuss the explicit example of the Schwarzschild spacetime and compare our result with the existing literature.