Thermodynamics of acoustic black holes in two dimensions

It is well-known that the thermal Hawking-like radiation can be emitted from the acoustic horizon, but the thermodynamic-like understanding for acoustic black holes was rarely made. In this paper, we will show that the kinematic connection can lead to the dynamic connection at the horizon between the fluid and gravitational models in two dimension, which implies that there exists the thermodynamic-like description for acoustic black holes. Then, we discuss the first law of thermodynamics for the acoustic black hole via an intriguing connection between the gravitational-like dynamics of the acoustic horizon and thermodynamics. We obtain a universal form for the entropy of acoustic black holes, which has an interpretation similar to the entropic gravity. We also discuss the specific heat, and find that the derivative of the velocity of background fluid can be regarded as a novel acoustic analogue of the two-dimensional dilaton potential, which interprets why the two-dimensional fluid dynamics can be connected to the gravitational dynamics but difficult for four-dimensional case. In particular, when a constraint is added for the fluid, the analogue of a Schwarzschild black hole can be realized

Hawking radiation and stability of the canonical acoustic black holes

In this paper we determine the Hawking temperature and entropy of a modified canonical acoustic black hole. In our results we obtain an area entropy, a correction logarithmic in leading order. We also analyze the stability condition of the noncommutative canonical acoustic black hole and also with quantum corrections implemented by the generalized Heisenberg uncertainty principle.Comment: 8 pages, no figure