On an approach to constructing static ball models in General Relativity

TL;DR

This paper presents a method for constructing static fluid ball models in General Relativity, including exact solutions and models involving special functions like Airy, hypergeometric, and Heun functions.

Contribution

It introduces a novel approach to static fluid ball modeling in General Relativity, incorporating exact solutions and special functions.

Findings

Two exact solutions of Einstein equations for fluid balls.

Models involving Airy, hypergeometric, and Heun functions.

Demonstration of the approach with five examples.

Abstract

An approach to construction of static models is demonstrated for a fluid ball. Five examples are considered. Two of them are exact solutions of the Einstein equations; the other three are connected with the Airy special functions, the hypergeometric functions and the Heun functions.