Hydrodynamic correlation functions

I am trying to understand in detail how one can compute correlation functions of the stress-energy tensor in relativistic fluids and solids. I have found a reference that explains in general terms how to do it [1205.5040]: simply include the metric as a source and solve the equations of motion in the presence of said sources.

I have two questions:

(1) Does anyone know of a resource that explains how to do this calculation in detail? I am finding that reproducing the results of [1205.5040] (see section 2.6) is quite tedious and I keep getting the wrong answer.

(2) Has this calculation been performed for solids? And are there any good resources for this calculation?