Acoustic horizons for axially and spherically symmetric fluid flow

Abstract

We investigate the formation of acoustic horizons for an inviscid fluid moving in a pipe in the case of stationary and axi-symmetric flow. We show that, differently from what is generally believed, the acoustic horizon forms in correspondence of either a local minimum or maximum of the flux tube cross-section. Similarly, the external potential is required to have either a maximum or a minimum at the horizon, so that the external force has to vanish there. Choosing a power-law equation of state for the fluid, $P\propto {\rho }^n$, we solve the equations of the fluid dynamics and show that the two possibilities are realized respectively for $n>-1$ and $n<-1$. These results are extended also to the case of spherically symmetric flow.

6 pages, 3 figures

References in corpus (9)

• Analogue Gravity
• Gibbons-Hawking Effect in the Sonic de Sitter Space-Time of an Expanding Bose-Einstein-Condensed Gas
• Quasinormal modes and classical wave propagation in analogue black holes
• "Cosmological" quasiparticle production in harmonically trapped superfluid gases
• Quasinormal modes and stability of the rotating acoustic black hole: numerical analysis
• Causal structure of acoustic spacetimes
• Quasinormal Ringing for Acoustic Black Holes at Low Temperature
• Acoustic analogs of two-dimensional black holes
• Acoustic analogues of black hole singularities

Cited by in corpus (3)

• Quasinormal modes of black holes and black branes
• Analogue Gravity
• Gravity as emergent phenomena for spherically symmetric black hole accretion of multi-component flow with relativistic equation of state