White dwarfs in a uniform sphere approximation, with general relativity effects taken into account

TL;DR

This paper investigates the maximum mass of white dwarfs using a uniform sphere model that incorporates general relativity and finite temperature effects, providing analytical formulas and numerical solutions.

Contribution

It introduces a uniform sphere approximation for white dwarfs that includes general relativity and finite temperature effects, with analytical and numerical solutions.

Findings

Analytical formulas for white dwarf models with relativistic effects

Numerical solutions closely match exact models within 20%

Finite temperature influences on white dwarf mass limits

Abstract

The limiting mass of cold white dwarfs was first calculated by E. Stoner in an approximate model of a uniform star and was soon reduced by ~20% in papers by S. Chandrasekhar and L. D. Landau based on an exact solution of the equations for the stellar equilibrium. Here we examine uniform models of white dwarfs taking general relativity effects and the influence of finite temperature into account. Solutions are obtained in the form of finite analytic formulas and, for masses differing by no more than ~20% from the exact solutions, found by numerical integration of the differential equations for the stellar equilibrium.