Hawking radiation from acoustic black holes in two space dimensions

We study the Hawking radiation for the acoustic black hole. In the beginning, we follow the outline of Jacobson but then we use a different 2 + 1 vacuum state similar to the vacuum state constructed by Unruh. We also use a special form of the wave packets. The focus of the paper is to treat the 2-dimensional case, in particular, the case when the radial and angular velocity are variable.