Sound modes in holographic superfluids

Superfluids support many different types of sound waves. We investigate the relation between the sound waves in a relativistic and a non-relativistic superfluid by using hydrodynamics to calculate the various sound speeds. Then, using a particular holographic scalar gravity realization of a strongly interacting superfluid, we compute first, second and fourth sound speeds as a function of the temperature. The relativistic low temperature results for second sound differ from Landau's well known prediction for the non-relativistic, incompressible case.