On the Classical and Quantum Irrotational Motions of a Relativistic Perfect Fluid. I. Classical Theory

Some aspects of perfect-fluid general-relativistic hydrodynamics under the assumptions of irrotationality and isentropicity are analysed. A new derivation of the known fact that the Lagrangian for these fluids is just the pressure is given. Then we study the fluctuations around a given background field configuration, extracting a rule that connects the order at which a Taylor expansion of the action functional possibly stops with the fluid equation of state. From a classical invariance of the action we deduce the conserved Noether current. Because of the spontaneous breaking of such an invariance on the vacuum state Goldstone bosons arise, which turn out to be just phonons (quantized sound waves). Some useful results concerning the linear theory of sound waves are also given.