Acoustic Black Holes

Acoustic propagation in a moving fluid provides a conceptually clean and powerful analogy for understanding black hole physics. As a teaching tool, the analogy is useful for introducing students to both General Relativity and fluid mechanics. As a research tool, the analogy helps clarify what aspects of the physics are kinematics and what aspects are dynamics. In particular, Hawking radiation is a purely kinematical effect, whereas black hole entropy is intrinsically dynamical. Finally, I discuss the fact that with present technology acoustic Hawking radiation is almost experimentally testable. To appear in the Proceedings of the 1998 Peniscola Summer School on Particle Physics and Cosmology. (Springer-Verlag). 1 Developing the analogy To ask how sound waves propagate in a moving fluid is a surprisingly subtle question that rapidly introduces one to the full power and complexity of curved-space Lorentzian differential geometry [1,2,3,4,5,6,7]. A sound wave propagating in a flowing fluid shares many of the properties of a minimally coupled massless scalar field propagating in a non-flat (3+1)–dimensional Lorentzian geometry. This partial isomorphism is the basis of a very useful analogy whereby parts of General Relativity can be identified with parts of non-relativistic fluid mechanics. Kinematic aspects of GR, such as the existence of event horizons, carry over to fluid mechanics (event horizons map into the boundaries of regions of supersonic flow). Dynamic aspects of GR (the Einstein equations) do not carry over. The analogy is not an identity, nevertheless enough features are shared in common to make the model very useful, and rather entertaining. (Since this is a summer school, I will be very pedagogical and will set out a number of exercises as we work through the details.) 1.1 Ingredients The basic idea is to consider a non-relativistic, irrotational, barotropic fluid. The fluid should be irrotational since in this case the velocity is completely specified by a scalar field, (which does not have to be single-valued): ∇× v = 0; ⇒ v = ∇ψ. (1) Thus there is hope that the sound waves, which we shall soon see are merely linearized fluctuations in the velocity field, can also be described by a scalar