Analog Schwarzschild black hole from a nonisentropic fluid

TL;DR

This paper explores how a relativistic fluid can mimic Schwarzschild black hole geometry through analog acoustic metrics, revealing that such an analogy requires the speed of sound to equal light speed, which limits the analogy behind the horizon.

Contribution

It demonstrates the conditions for a relativistic fluid to produce an analog Schwarzschild black hole geometry, highlighting the fundamental limitations imposed by relativistic constraints.

Findings

Speed of sound must equal the speed of light for the analogy.

Analog Schwarzschild geometry breaks down behind the horizon.

Relativistic fluid cannot fully replicate black hole interior geometry.

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.