New Symmetry for the Imperfect Fluid in Relativistic Astrophysics

ABSTRACT A new symmetry is presented for the case of imperfect fluids with vorticity in gravitational fields making use of the new tetrads previously introduced. We prove that this symmetry is a local symmetry of the metric tensor for a general imperfect fluid with vorticity. Therefore we conclude that the left hand side of the Einstein‐Fluid equations is invariant under this local symmetry. This new symmetry is completely analogous to the local electromagnetic gauge symmetry in the sense that arises when the fluid four‐velocity vectors are transformed into four‐velocity vectors plus a local gradient of a local scalar function. The stress‐energy tensor cannot be invariant only under this transformation. In order to make the stress‐energy invariant under this local Abelian group, additional transformations are proposed for the energy density, pressure, the heat flow and viscous stresses. It is found the form of all of these proposed transformations by imposing invariance on the whole stress‐energy tensor. As a byproduct we can use this symmetry to introduce a stress‐energy tensor for vorticity invariant under the four‐velocity gauge‐like group of transformations. Applications in astrophysical evolution are developed for the neutron star superfluid that possesses large scale vorticity.