Vol. 7, Issue 2, Part C (2025)

Main peculiarities of formulation main principles and criteria of white dwarf theories are analyzed. Short comparative analysis of main methods of modeling is represented. All these methods are based on the conditions of equilibrium. The role of A. Eddington, R. Fowler, E. Stoner and S. Chandrasekar researches in the creation this theory is discussed. A. Eddington proposed to use the Lane-Emden equations to construct the theory of white dwarfs, which allow us to describe processes in polytropic gas spheres. It is shown that Stoner method, Lane-Emden equations and Einstein equations is based on the search of equilbrium comditions for sphere or semple to sphere symmetries. The role of the development of theoretical physics (Fermi-Dirac statistics) in the creation of this theory is shown. It should be noted that thanks to Stoner's research, the Pauli principle and one of the first applications of Fermi-Dirac statistics for degenerate electronic systems appeared in the Bohr theory of the atom precisely in the theory of white dwarfs. Main peculiarities of Stoner method and Lane-Emden equtions are observed. Stoner's method is based on the idea of studying the equilibrium of a star based on energetic considerations. The Lane-Emden equations were constructed for gaseous spheres with different polytropic indices. It was Emden's introduction of thermodynamics into these equations that allowed them to be used in astrophysics. For these equations, it is necessary to additionally introduce the conditions for the rotation of the star. Einstein's equation is also on the one hand a condition of energy equilibrium for inhomogeneous systems, and on the other hand it is a generalization of the special theory of relativity to curvilinear geometry. Rotation is included in the equation from the very beginning. Peculiarities of application methods of general relarivity for modelling white dwarf structure and processes are analyzed too.