A relativistic acoustic metric for planar black holes

TL;DR

This paper shows that the metric of a planar black hole in Anti-de Sitter space can be represented as a relativistic acoustic metric, extending previous non-relativistic results and providing a concrete Lagrangian form.

Contribution

It introduces a relativistic acoustic metric representation for planar black holes, advancing the understanding of black hole analogs in relativistic fluid systems.

Findings

Relativistic acoustic metric reproduces planar black hole geometry.

Provides a concrete Lagrangian for the relativistic acoustic model.

Completes the transition from non-relativistic to relativistic descriptions.

Abstract

We demonstrate here that the metric of a planar black hole in asymptotic Anti-de Sitter space can, on a slice of dimension 3+1, be reproduced as a relativistic acoustic metric. This completes an earlier calculation in which the non-relativistic limit was used, and also serves to obtain a concrete form of the Lagrangian.