On space-time permeated by the relativistic charged fluid

The behaviour of the self-gravitating charged fluid with constant electric conductivity and constant magnetic permeability is investigated by choosing a suitable orthonormal tetrad frame. The properties of the charged fluid with the electric field orthogonal to the magnetic field admitting groups of motion with respect to the flow vector are studied. It is proved that this fluid degenerates into nonconducting fluid if it allows groups of motion with respect to its flow vector. Moreover, for the convention-free charged fluid with electric field orthogonal to the magnetic field a necessary and sufficient condition for null conductivity is found