Nonlinear variations in spherically symmetric accretion in the Schwarzschild metric

TL;DR

This paper investigates how nonlinear effects influence spherically symmetric accretion flows in a Schwarzschild spacetime, revealing potential instabilities overlooked by linear analysis.

Contribution

It introduces a nonlinear perturbation framework for relativistic accretion and shows that nonlinearities can destabilize solutions previously considered stable.

Findings

Linear stability may not hold when nonlinear effects are included.

Nonlinearities can lead to instability in otherwise stable accretion flows.

The perturbation equation resembles Liénard's equation, indicating complex dynamical behavior.

Abstract

In this work, we study the implications of nonlinearity in general relativistic spherically symmetric inviscid irrotational accretion flow in a stationary non-rotating spacetime. It has been found that the perturbation scheme leads to a differential equation of the form of general Li{\'e}nard's equation. We discuss the equilibrium conditions of this system and its implications for globally subsonic accretion flows in the spherically symmetric stationary background. It is found that the stable solution predicted by linear stability analysis may become unstable under inclusion of lowest order nonlinearity.