Dual Physical Interpretations of the Energy Tensor in General Relativity.
Here I investigate the possibility of dual physical interpretations of the energy tensor in General Relativity, i.e. that a particular form might correspond to more than one physical kind of matter field. "Plausibility" is developed as the criterion for arguing whether such dual interpretations should be deemed viable. I study the electromagnetic and imperfect fluid energy tensors, these being the most prevalent classical fields. The algebraic Rainich conditions are applied to the fluid. Characteristics and equations of state are analyzed. While requiring a relativistic fluid of peculiar properties, a dual interpretation is not prohibited. Conduction is shown to be generally necessary, and analogous to the Poynting vector. Large viscosity effects are always necessary, showing that the common "photon gas/null fluid" models for e.m. fields are not correct. Exact relations between fluid and e.m. parameters are then found, via an alternate e.m. energy tensor. This identifies the relationships between basic quantities of both fields, relating them to fluid rest-frame invariants. All algebraic requirements are satisfied. Viscous fluids as a special case are shown to require diagonal fluid rest -frame energy tensor. Examples of known electromagnetic metrics are tested as an equivalent fluid. Viscous identifications are shown to fail for all cases studied. The Kerr-Newman solution is internally contradictory, its Poynting vector is incompatible with vanishing conduction. The Reissner -Nordstrom solution also fails, despite zero energy transport, since its fluid dynamical behavior violates the energy conditions. I suggest that all dual e.m. fluids might prove dynamically implausible, and outline how to develop necessary criteria. I point out topics for which results found here must prove significant, mainly astophysical models based on the null fluid, and discuss probable effects.
- Pub Date:
- Physics: Fluid and Plasma