Perturbations on steady spherical accretion in Schwarzschild geometry

TL;DR

This paper investigates how the coupling of spherically symmetric accretion flows with Schwarzschild spacetime affects stability, showing enhanced damping of perturbations and implications for acoustic metrics.

Contribution

It demonstrates that space-time coupling increases flow stability and prevents defining an acoustic metric in Schwarzschild geometry, contrasting with Newtonian predictions.

Findings

Perturbations decay over time in Schwarzschild geometry.

Coupling with space-time enhances flow stability.

No acoustic metric can be defined for the flow in Schwarzschild spacetime.

Abstract

The stationary background flow in the spherically symmetric infall of a compressible fluid, coupled to the space-time defined by the static Schwarzschild metric, has been subjected to linearized perturbations. The perturbative procedure is based on the continuity condition and it shows that the coupling of the flow with the geometry of space-time brings about greater stability for the flow, to the extent that the amplitude of the perturbation, treated as a standing wave, decays in time, as opposed to the amplitude remaining constant in the Newtonian limit. In qualitative terms this situation simulates the effect of a dissipative mechanism in the classical Bondi accretion flow, defined in the Newtonian construct of space and time. As a result of this approach it becomes impossible to define an acoustic metric for a conserved spherically symmetric flow, described within the framework of Schwarzschild geometry. In keeping with this view, the perturbation, considered separately as a high-frequency travelling wave, also has its amplitude reduced.