arXiv subjects

Parker Hund

Publications and source records attributed to Parker Hund.

4 recordsLinked to original sources

arXiv2022

A Two Species Thomas-Fermi Model for Stellar Ground States

We present an energy functional for a Thomas-Fermi type two-fluid model of a self-gravitating non-rotating charged body, with a non-relativistic kinetic energy. We prove that, under certain conditions on the total number of positively charged and negatively charged particles, a minimizer exists and both fluids have compact support. We prove the same result for special relativistic kinetic energy, assuming further conditions on the total number of particles. In the non-relativistic kinetic energy case, we further prove the uniqueness of the minimizer, as well as present results relating the general shape of the minimizer to the total number of particles.

math-ph↗

arXiv2021

General Relativistic Non-Neutral White Dwarf Stars

We generalize the recent Newtonian two-component charged fluid models for white dwarf stars of Krivoruchenko, Nadyozhin and Yudin and of Hund and Kiessling to the context of general relativity. We compare the equations and numerical solutions of these models. We extend to the general relativistic setting the non-neutrality results and bounds on the stellar charge obtained by Hund and Kiessling.

gr-qc↗

arXiv2021

Electrically non-neutral ground states of stars

To approximately compute the non-relativistic ground state of an electrically non-neutral star, an exactly solvable model was recently introduced, and partly solved, by Krivoruchenko, Nadyozhin, and Yudin. The model generalizes the well-known Lane--Emden equation of a polytropic gas ball of index $n=1$ to a two-fluid setting. Here its complete solution is presented in terms of simple elementary functions; it is also generalized to a more-than-two-fluid setting where it remains exactly solvable. It is shown that, given the number of nuclei, a maximal negatively and a maximal positively charged solution exists, plus a continuous family of solutions which interpolates between these extremes. Numerical comparisons show that this exactly solvable model captures the qualitative behavior of the more physical model it is supposed to approximate. Furthermore, it correctly answers the question: how non-neutral can the star be? The answer is independent of the speed of light $c$ and the Planck quantum $h$. It supports Penrose's weak cosmic censorship hypothesis, in the sense that the bounds on the excess charge are compatible with the bound on the charge of a Reissner--Weyl--Nordström black hole.

gr-qc↗

arXiv2020

How much electric surcharge fits on ... a white dwarf star?

The question how much surplus of electric charge ("surcharge") fits on an object is generally very difficult to answer. Here it is shown that it is easy to answer when the object is a \emph{failed white dwarf} star (a brown dwarf in its ground state) made of protons and electrons: Given the number of protons, how many electrons can there be? Surprisingly, the answer (in the form: as few as $\mathfrak{A}$ and as many as $\mathfrak{B}$) is independent of the speed of light $c$ and the Planck quantum $h$, even when the star is stabilized against collapse by relativistic quantum mechanics.

gr-qc↗