Analog Schwarzschild Black Hole from a Nonisentropic Fluid

Neven Bilić,Hrvoje Nikolić

doi:10.3390/universe7110413

Abstract

We study the conditions under which an analog acoustic geometry of a relativistic fluid in flat spacetime can take the same form as the Schwarzschild black hole geometry. We find that the speed of sound must necessarily be equal to the speed of light. Since the speed of the fluid cannot exceed the speed of light, this implies that analog Schwarzschild geometry necessarily breaks down behind the horizon.

Highlights

The analog acoustic metric was first introduced by Unruh [1], with the motivation of explaining the Hawking radiation produced by black holes [2]
By making use of nonisentropic fluid dynamics, we have succeeded in modeling an analog of the Schwarzschild spacetime
Applying an analog metric in the form similar to the metric in Painlevé–Gullstrand coordinates, we have been able to reproduce the exterior of a Schwarzschild black hole in the limit when the speed of sound approaches the speed of light

Summary

Introduction

The analog acoustic metric was first introduced by Unruh [1], with the motivation of explaining the Hawking radiation produced by black holes [2]. The fluid is assumed to satisfy the Euler equation without external pressure, and particle number conservation is assumed With these assumptions, the acoustic metric of the form (1), which mimics the Schwarzschild black hole, cannot be found. It has been noted that a nonrelativistic version of the metric (1) can be found, which differs from the Schwarzschild metric by a non-constant conformal factor [3,4,15] Even in this case, one must assume an external force field to satisfy the Euler equation. Since the acoustic horizon is by definition a surface beyond which the fluid is faster than the speed of sound, it follows that the fluid beyond the horizon should be superluminal, which is physically forbidden This means that analogue metric can take the form of a Schwarzschild geometry only outside of the black hole, and not in the black hole interior.

Analog Schwarzschild Geometry

Field Theoretic Description of the Nonisentropic Fluid Flow

Conclusions