Heat conduction in general relativity

We study the problem of heat conduction in general relativity by using Carter's variational formulation. write creation rates entropy and particle as combinations vorticities temperature chemical potential. pay attention to fact that there are two additional degrees freedom choosing relativistic analog Cattaneo equation for parts binormal caloric number flows. Including contributions from parts, we find a $\textit{new}$ heat-flow equations discover their dynamical role thermodynamic systems. The benefit introducing is it allows room physical ansatz describing whole evolution system. Taking advantage this platform, propose proper deals with starting properties thermal equilibrium also consider stability system flat background. "Klein" modes exist addition known ones. requirement less stringent than those literature.