Abstract. We present a general method for constructing acoustic analogues 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 also be 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 a 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 = T dS 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.

PACS numbers: 04.70.Dy, 47.40.Ki

Print publication: Issue 2 (21 January 2005)
Received 12 November 2004, in final form 1 December 2004
Published 29 December 2004