Rotational motion of a stationary axisymmetric relativistic heat conducting fluid configuration

Abstract

The present work describes some dynamical features associated with the dissipation caused by the heat flow in the context of rotational motion of a heat conducting fluid based on Carter’s two-fluid model. A covariant solutions to a pair of Maxwell’s like equations governing the evolution of a heat conducting fluid are used to determine the heat flow vector and the matter part of fluid’s 4-velocity under the assumption that the space-time configuration representing the gravitational field of a heat conducting fluid is non-circular stationary and axisymmetric. These results are used to derive the rotational velocity in terms of gradients of the effective energy and effective angular momentum per particle. It is demonstrated that the meridional circulations of the matter part of fluid induce the rotational velocity in addition to the usual rotational velocity found in a circular space-time. It is shown that the differential rotation along the thermal –fluid vorticity causes the twist of matter part of fluid’s vortex lines in addition to the other effects .It is found that the gravitational isorotation is balanced by counter rotating thermal isorotation in the case of differentially rotating thermal-fluid surfaces in a frame of reference in which thermal –fluid helicity is conserved. The dynamic interaction between the matter part of fluid and the entropy fluid leads to the mutual exchange between the energy and angular momentum per baryon of the matter part of fluid and the flux of energy and angular momentum per entropon per unit of local temperature coupled to heat flow vector created by the entropy fluid.