2023/06/29 by Shuichi Yokoyama, Yokoyama, Shuichi · 1 citation
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Astrophysical Phenomena (astro-ph.HE) #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Solar and Stellar Astrophysics (astro-ph.SR) #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.2306.16647
openalex publication_date 2023/06/29 · openalex created_date 2023/07/01 · openalex updated_date 2026/07/28
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.