On an Extension of a Static Ball Solution

TL;DR

This paper presents a new exact static interior solution to Einstein's equations for a perfect fluid sphere, extending classical models to describe more compact objects like neutron stars, with a novel mass density cusp behavior.

Contribution

It introduces an extended static interior solution for gravitating balls with perfect fluid, capturing more realistic dense astrophysical objects and revealing a cusp catastrophe near the center.

Findings

Provides a new exact solution for compact stars.

Describes a mass density cusp near the stellar center.

Extends classical interior solutions to more realistic models.

Abstract

A new exact static interior solution of the Einstein equations is obtained for a gravitating ball filled with a Pascal perfect fluid . The solution is an extension of the well-known interior solution with a parabolic distribution of mass density and describes more compact astrophysical objects such as neutron and hyperon stars. It is shown that a behaviour of the new mass density distribution near the stellar centre can be described as a cusp catastrophe.