Jaumann transport in relativistic continuum mechanics

The Jaumann derivative of a tensor field in relativity is defined by a formal generalization of a stress rate in viscoelasticity. A tensor field is said to be Jaumann transported if 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-Newmann black hole into the Reissner-Nordstrom black hole is expressed in terms of the Jaumann propagation. (author)