Relativistic Hydrostatic Structure Equations and Analytic Multilayer Stellar Model

TL;DR

This paper develops a complete set of relativistic hydrostatic structure equations for stars, derives exact forms of related equations in curved spacetime, and demonstrates their application to multilayer stellar models with analytic solutions.

Contribution

It introduces a relativistic extension of stellar structure equations, including the TOV and temperature equations, and provides analytic multilayer stellar models with potential applications to stars like the Sun.

Findings

Exact relativistic Poisson and heat conduction equations derived.

Heat capacity ratio approaches one in convection zones.

Analytic multilayer stellar models including the Sun proposed.

Abstract

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.