Dynamics of a perfect fluid through velocity potentials with aplication in quantum cosmology

TL;DR

This paper reviews scalar potential formalisms for perfect fluid hydrodynamics and discusses their application in quantum cosmology, particularly how Schutz's formalism introduces a time variable in minisuperspace models.

Contribution

It compares classical and relativistic formalisms for perfect fluids and demonstrates their use in quantum cosmology to incorporate time.

Findings

Scalar potentials effectively describe perfect fluid dynamics.

Schutz's formalism enables a phenomenological time variable in quantum cosmology.

The Hamiltonian formulation facilitates quantum analysis of cosmological models.

Abstract

We review the Eulerian description of hidrodynamics using Seliger-Whitham's formalism (in classical case) and Schutz's formalism (in relativistic case). In these formalisms, the velocity field of a perfect fluid is described by scalar potentials. With this we can obtain the evolution equations of the fluid and its Hamiltonian. In the scenario of quantum cosmology the Schutz's formalism makes it possible to introduce phenomenologically a time variable in minisuperspace models.