Regular Article - Theoretical Physics
New symmetry for the imperfect fluid
Former Professor at Universidad de la República, Av. 18 de Julio 1824-1850, 11200, Montevideo, Uruguay
* e-mail: email@example.com
Accepted: 29 March 2020
Published online: 21 April 2020
We will address the existence of a new symmetry for an imperfect fluid by introducing local four-velocity gauge-like transformations for the case when there is vorticity. A similar tetrad formulation as to the Einstein–Maxwell spacetimes formalism presented in previous manuscripts will be developed in this manuscript for the imperfect fluids. The four-velocity curl and the metric tensor will be invariant under these kind of four-velocity gauge-like local transformations. While the Einstein–Maxwell stress-energy tensor is locally gauge invariant under electromagnetic gauge transformations, the perfect fluid stress-energy tensor will not be invariant under four-velocity gauge-like local transformations. We will dedicate our analysis to the imperfect fluid stress-energy tensor that will be invariant under local four-velocity gauge-like transformations when additional transformations are introduced for several variables included in the stress-energy tensor itself. We will also pay special attention to the construction of a vorticity stress-energy tensor invariant under local four-velocity gauge-like transformations. An application on neutron stars will be developed in order to show the simplifications brought about by these new tetrads.
© The Author(s), 2020