Hydrostatic equilibrium of stars without electroneutrality constraint

Abstract

The general solution of hydrostatic equilibrium equations for a two-component fluid of ions and electrons without a local electroneutrality constraint is found in the framework of Newtonian gravity theory. In agreement with the Poincaré theorem on analyticity and in the context of Dyson's argument, the general solution is demonstrated to possess a fixed (essential) singularity in the gravitational constant G at G = 0. The regular component of the general solution can be determined by perturbation theory in G starting from a locally neutral solution. The non-perturbative component obtained using the method of Wentzel, Kramers and Brillouin is exponentially small in the inner layers of the star and grows rapidly in the outward direction. Near the surface of the star, both components are comparable in magnitude, and their non-linear interplay determines the properties of an electro-or ionosphere. The stellar charge varies within the limits of −0.1 to 150 C per solar mass. The properties of electro-and ionospheres are exponentially sensitive to variations of the fluid densities in the central regions of the star. The general solutions of two exactly solvable stellar models without a local electroneutrality constraint are also presented.

On holomorphic regularization of strongly nonlinear singularly perturbed problems

“…In theoretical physics, a so-called Dyson's argument is known [8]. It expresses the property of non-analiticity for solution to each (in the general case) singularly perturbed problem and following Poincaré theorem on expansion.…”

Axiomatic Approach in the Analytic Theory of Singular Perturbations

“…This is very urgent since the range of problems leading to singularly perturbed problems is constantly expanding. In this sense, the "Dyson argument" that appeared in theoretical physics is quite indicative-the solutions of the equations arising in astrophysics can depend holomorphically on the gravitational constant only after isolating a revealing the essentially singular manifold [7].…”

Structure of Relativistic Stars Composed of Incompressible Matter in the Absence of Strict Electroneutrality

“…The structure of stars in the absence of LEN was considered in a number of papers (see, e.g., Bally and Harrison 1978;Neslusan 2001;Iosilevskiy 2009). Krivoruchenko et al (2018) explored the topic under consideration in the Newtonian approximation using two-component polytropic stellar models. The complete solution determining the stellar structure turned out to consist of two parts: a regular part that can be represented as a series in the small parameter 1/Λ G with the LEN solution as the zeroth approximation and an irregular part that is exponentially small everywhere, except for a finite number of zones usually located at the boundary of the domain of integration (the so-called boundary layer).…”

“…However, the deviations from LEN are small even in the complete solution obtained, LEN is strongly violated only in a thin surface layer (the so-called "electrosphere"), the polarization field is everywhere small, and This paper is the first step in this direction. Using the previous experience (Krivoruchenko et al 2018) and the fundamental papers by Bailyn (1975, 1978), who derived the equilibrium equations for matter within the framework of general relativity in the absence of LEN, we managed to generalize the past calculations to the case of a multi-component fluid in general relativity. So far we have restricted our analysis to incompressible nuclear matter (the polytrope n = 0).…”