Thomas–Fermi model for a bulk self-gravitating stellar object in two dimensions

Abstract

In this article we have solved an hypothetical problem related to the stability and gross properties of two dimensional self-gravitating stellar objects using Thomas-Fermi model. The formalism presented here is an extension of the standard three-dimensional problem discussed in the book on statistical physics, Part-I by Landau and Lifshitz. Further, the formalism presented in this article may be considered as class problem for post-graduate level students of physics or may be assigned as a part of their dissertation project.

Approximate solution of a Thomas–Fermi model equation for bulk self-gravitating stellar objects in two dimensions

“…It is shown in [1] that the (normalized) Fermi energy density, here denoted y x ( ), in the non-relativistic case varies according to the following linear equation . This solution can then be used to determine the properties of the white dwarf e.g.…”

“…This solution can then be used to determine the properties of the white dwarf e.g. mass-radius relation and average density see [1].…”

“…Recently an introductory presentation was given of self-gravitating stellar objects using the Thomas-Fermi model equation for the Fermi energy density in two-dimensional radially symmetric geometry, see [1]. The properties of both non-relativistic and ultra-relativistic cases were studied and analysed.…”

“…The solution is well know: q w = t A t cos 0 ( ) ( ) where A denotes the oscillation amplitude. However, for large swinging angles, equation (1) has to be improved to read…”

“…The accuracy of the obtained approximate solutions can not be determined a priori and the studied equation has also to be solved numerically to assess the quality of the obtained solution. In order to demonstrate the usefulness and the capability of the Rayleigh-Ritz optimization procedure in a manner accessible for under-graduate and graduate students, we will, in the subsequent sections, analyse the Thomas-Fermi equations introduced and studied in [1].…”