Comment on "Analog Schwarzschild-like geometry in fluids with external pressure''

TL;DR

This paper critically examines previous claims about analogue models of black hole spacetimes in fluids, clarifying the role of external forces and pressure, and reaffirming the validity of earlier results with proper force modeling.

Contribution

It clarifies the conceptual correctness of external force modeling in analogue gravity models and defends previous findings against alternative pressure-based approaches.

Findings

External force modeling is conceptually correct when properly added.

Previous results on analogue Schwarzschild models remain valid.

Pressure-based external forces lead to inconsistencies with the continuity equation.

Abstract

In Ref. [1], exact (not only conformally related) analogue models for the Schwarzschild and Reissner-Nordstr\"om spacetimes were found. The background non-relativistic fluid flow was sustained by an external body force which is not affected by the linearised fluctuations. Following a different route, by modelling the external force as the gradient of an external pressure, it was shown in~\cite{bilic} that the speed of sound is significantly modified. This effective speed of sound turns out to be inconsistent with the continuity equation. In this comment we analyse these two contradictory conclusions. We first show that the heuristic justification for the introduction of the external force via a variational principle given in Ref. [2] is conceptually incorrect. Then, by adding the external force appropriately, we show that the conclusions in [1] remain valid.