Signature-Causality Reflection in An Imperfect Fluid with Vorticity Generated by Tetrad Abelian Gauge Transformations

Abstract

We will address the possibility of a change in signature-causality in an imperfect fluid when we consider four-velocity gauge-like transformations in the case when the fluid has vorticity. An analogous tetrad formulation as to the Einstein-Maxwell spacetimes formalism introduced previously. The curl of the four-velocity and also the metric tensor will be invariant under the group of four-velocity gauge-like local transformations. The Einstein-Maxwell stress-energy tensor is invariant under local electromagnetic gauge transformations, similarly the imperfect fluid stress-energy tensor will also be invariant under the group of four-velocity gauge-like local transformations when we consider additional variable transformations in the stress-energy tensor. However, there is a relevant local causality scalar that undergoes a change in sign due to reflections under appropriate local Abelian tetrad gauge transformations. In this note we will study how to produce a signature-causality reflection in a region of spacetime bounded by a closed null surface using this same kind of transformations. This will be an important result since it is a physical result obtained through the use of a new local scalar quantity.