  The relativistic extension of the classic stellar structure equations is
investigated. It is pointed out that the Tolman-Oppenheimer-Volkov (TOV)
equation with the gradient equation for local gravitational mass can be made
complete as a closed set of differential equations by adding that for the
Tolman temperature with one equation of state, and the set is proposed as the
relativistic hydrostatic structure equations. The exact forms of the
relativistic Poisson equation and the steady-state heat conduction equation in
the curved spacetime are derived. The application to an ideal gas of particles
with the conserved particle number current leads to a strong prediction that
the heat capacity ratio almost becomes one in any Newtonian convection zone
such as the solar surface. The steady-state heat conduction equation is solved
exactly in the system and thermodynamic observables exhibit the power law
behavior, which implies the possibility for the system to be a new model of
stellar corona and a flaw in the earlier one obtained by using the
non-relativistic stellar structure equations. The mixture with another ideal
gas yields multilayer structure to a stellar model, in which classic stellar
structure equations are reproduced and analytic multilayer structure of
luminous stars including the Sun is revealed in suitable approximation.
