Interior Static Stellar Model with Electric Charge as an Oscillator

TL;DR

This paper develops an exact solution framework for static charged stellar models in general relativity by reducing Einstein-Maxwell equations to a nonlinear oscillator form, enabling explicit solutions for certain energy density profiles.

Contribution

It introduces a novel approach of transforming Einstein-Maxwell equations into a harmonic oscillator form for static charged stars, providing explicit solutions for specific energy density laws.

Findings

Exact solutions for charged star models derived from oscillator equations

Reduction of Einstein-Maxwell equations to a nonlinear oscillator form

Explicit solutions for particular energy density distributions

Abstract

A model approach to the description of static stars filled with a charged Pascal perfect fluid within the framework of general relativity is investigated. The metric is written in Bondi's radiation coordinates. The gravitational equations are reduced to a nonlinear oscillator equation after transfomation to a new variable as a function of the radial coordinate. It is shown that in this case exact solutions of the Einstein-Maxwell equations for a concrete energy density distribution law of the charged fluid may be obtained as solution of the harmonic oscillator equation.