Analogue models for Schwarzschild and Reissner-Nordstr\"om spacetimes

TL;DR

This paper develops hydrodynamic analogue models for Schwarzschild and Reissner-Nordström black holes, where sound waves mimic scalar fields in these spacetimes, with flow velocity linked to black hole parameters.

Contribution

It introduces a novel hydrodynamic framework to simulate Schwarzschild and RN spacetimes using unidirectional flows, enabling experimental exploration of black hole physics.

Findings

Sound waves propagate as scalar fields in the analogue models.

Flow velocity magnitude correlates with black hole mass and charge.

Physical quantities remain finite at the analogue horizon.

Abstract

We present analogue models for the Schwarzschild and Reissner-Nordstr\"om (RN) spacetimes based on unidirectional hydrodynamic flows. We show that, with appropriate coordinate transformations, sound waves in a moving fluid propagate as scalar fields at the equatorial sections of Schwarzschild and RN black holes. The coordinate associated with the direction of the flow plays the role of the radial coordinate in standard Schwarzschild/RN coordinates, while the transversal spatial coordinate is related to the angular coordinate on each equatorial slice. The magnitude of the flow velocity is related to the mass and charge of the analogue black hole. Physical quantities like pressure and density remain finite at the analogue horizon, thereby resulting in sound waves that are well defined almost everywhere, except possibly at the analogue black hole singularity.