Generating perfect fluid spheres in general relativity

TL;DR

This paper introduces transformation theorems that systematically generate and classify all static perfect fluid spheres in general relativity, revealing new connections and solutions in the field.

Contribution

The paper develops new transformation theorems that map and classify perfect fluid spheres, providing a systematic framework for understanding these solutions.

Findings

New transformation theorems linking perfect fluid spheres

Discovery of previously unknown perfect fluid sphere solutions

Uncovering unexpected relationships between known solutions

Abstract

Ever since Karl Schwarzschild's 1916 discovery of the spacetime geometry describing the interior of a particular idealized general relativistic star -- a static spherically symmetric blob of fluid with position-independent density -- the general relativity community has continued to devote considerable time and energy to understanding the general-relativistic static perfect fluid sphere. Over the last 90 years a tangle of specific perfect fluid spheres has been discovered, with most of these specific examples seemingly independent from each other. To bring some order to this collection, in this article we develop several new transformation theorems that map perfect fluid spheres into perfect fluid spheres. These transformation theorems sometimes lead to unexpected connections between previously known perfect fluid spheres, sometimes lead to new previously unknown perfect fluid spheres, and in general can be used to develop a systematic way of classifying the set of all perfect fluid spheres.