Second Order Perturbative Effects on the Acoustic Geometry

Abstract

In this work, we have studied the effect of higher order perturbations, particularly the second order in details, on the sonic horizon. We have considered two different schemes of perturbations which are velocity potential perturbation and mass acceleration rate perturbation. These two schemes give us qualitatively similar behaviour. We have found that the analogue gravity formalism also holds for the higher order perturbations.

Latex 2e, 9 pages