Analog Schwarzschild black hole from a nonisentropic fluid

Abstract

We study 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 fluid cannot exceed the speed of light, this implies that analog Schwarzschild geometry necessarily breaks down behind the horizon.

Analog Schwarzschild-like geometry in fluids with external pressure

“…[8], one has more flexibility. However, in a recent paper [9] it was shown that the Schwarzschild metric could be reproduced in a non-isentropic fluid only in the stiff-fluid limit when the sound speed approaches unity. De Oliveira et al [10] have recently obtained a closed-form expression for an analog Schwarzschild metric in NR setup with a non-constant speed of sound and a nonzero external pressure.…”