Euler observers for the perfect fluid without vorticity.

The perfect fluid was already studied for the case where there is vorticity. A new technique was developed in order to locally and covariantly diagonalize the perfect fluid stress-energy tensor. New tetrads were introduced to this purpose. In this
manuscript we will analyze the case where there is no vorticity. We will show how to implement for this case the diagonalization algorithm previously built for the case with vorticity. A novel technique will be introduced based only on purely geometrical
objects. As an application, a new algorithm will be formulated with the aim of finding Euler observers for this case without vorticity.