Jaumann transport in relativistic continuum mechanics

We define the Jaumann derivative of a tensor field in relativity by a formal generalization of a stress rate in viscoelasticity. A tensor field is said to be Jaumann transported iff its Jaumann derivative vanishes. It is found that the gravitational potentials are Jaumann transported identically. The concept of a complete rotation tensor has been introduced to study the Jaumann derivative with respect to a null vector field. This provides a characterization of the integrability of a hypersurface orthogonal congruence. A perfect fluid collapsing by neutrino emission and undergoing Jaumann transport with respect to the neutrino flow is found to be compatible with that of a catastrophic collapse. The circumstances leading to the existence of ghost neutrinos are cited. The degeneracy of the Kerr-Newman black hole into the Reissner-Nordstrom black hole is expressed in terms of the Jaumann propagation.