An interior solution of constant density to Gurses metric

TL;DR

This paper presents an interior solution for a sphere of electrically counterpoised dust with constant density that matches the Gurses metric, using the Lane-Emden equation for derivation.

Contribution

It introduces a new interior metric solution for ECD matching the Gurses metric, employing the Lane-Emden equation for the first time in this context.

Findings

Derived a consistent interior solution for ECD with constant density.

Successfully matched the interior solution to the Gurses metric.

Demonstrated the applicability of the Lane-Emden equation in this setting.

Abstract

We give here an interior metric which matches Gurses metric. The metric given here is a sphere of electrically counterpoised dust (ECD) of constant density. We use Lane Emden equation for obtaining the interior solution.