Acoustic analogs of two-dimensional black holes

Abstract

We present a general method for constructing acoustic analogs of the black hole solutions of two-dimensional (2D) dilaton gravity. Because by dimensional reduction every spherically symmetric, four-dimensional (4D) black hole admits a 2D description, the method can be also used to construct analogue models of 4D black holes. We also show that after fixing the gauge degrees of freedom the 2D gravitational dynamics is equivalent to an one-dimensional fluid dynamics. This enables us to find a natural definition of mass $M$, temperature $T$ and entropy $S$ of the acoustic black hole. In particular the first principle of thermodynamics $dM=TdS$ becomes a consequence of the fluid dynamics equations. We also discuss the general solutions of the fluid dynamics and two particular cases, the 2D Anti-de sitter black hole and the 4D Schwarzschild black hole.

some references added

References in corpus (3)

• Gibbons-Hawking Effect in the Sonic de Sitter Space-Time of an Expanding Bose-Einstein-Condensed Gas
• "Cosmological" quasiparticle production in harmonically trapped superfluid gases
• Causal structure of acoustic spacetimes

Cited by in corpus (15)

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• Synthetic gravitational horizons in low-dimensional quantum matter
• Quasinormal Ringing for Acoustic Black Holes at Low Temperature
• Acoustic analogues of black hole singularities
• Thermodynamic duality between RN black hole and 2D dilaton gravity
• Aharonov-Bohm effect for a fermion field in a planar black hole "spacetime"
• Thermodynamics of acoustic black holes in two dimensions
• Acoustic horizons for axially and spherically symmetric fluid flow
• See a Black Hole on a Shoestring
• A note on analogue semi-classical gravity in (1+1) dimensions
• Two-dimensional description of D-dimensional static black holes with pointlike sources