# Second Order Perturbative Effects on the Acoustic Geometry

## TL;DR

This paper investigates how second order perturbations affect the acoustic geometry and sonic horizon, demonstrating that the analogue gravity formalism remains valid at higher perturbation orders.

## Contribution

It provides a detailed analysis of second order effects on acoustic geometry using two perturbation schemes, extending the validity of the analogue gravity formalism.

## Key findings

- Higher order perturbations influence the sonic horizon.
- Analogue gravity formalism remains valid for second order perturbations.
- Velocity potential and mass acceleration rate perturbations show similar behavior.

## 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.