• quantum field theory in curved spacetime
• analogue gravity
• Hawking radiation
• horizon thermodynamics

In this thesis work, we approach the fluid dynamics by means of a covariant formalism based on kinetic theory. At first, we deal with the model of a spherical
acoustic hole, simulating the Schwarzschild metric in 3+1 dimensions. We will present
an original calculation for the Hawking temperature under the educated guess that the
area law holds also for acoustic holes. The intimate relation between the Hawking
emission and the horizon area, that has been proven for black holes, is here highlighted
also for the acoustic holes, allowing the derivation of the Hawking temperature for relativistic fluid.
Once the area law is derived for acoustic holes, we move to calculate by the same approach the shear viscosity at the acoustic hole horizon beyond equilibrium. To this aim,
we model a shear perturbation of an acoustic horizon as a simulated gravitational wave,
realized via sound speed modulation. In gravity and in theories dual to gravity,
the ratio between the shear and the entropy density has been predicted to be equal to
the universal value (KSS ratio), so that we comment our results against this prediction.