Gravitational fields of rotating disks and black holes

TL;DR

This paper discusses exact solutions to Einstein's field equations for rotating black holes and disks, unifying them through a common mathematical framework involving Jacobi's inversion problem and extending to differentially rotating disks.

Contribution

It introduces a unified mathematical framework for known and new solutions describing rotating astrophysical objects in general relativity.

Findings

Black hole and disk solutions are represented in a common form.

A new family of solutions for differentially rotating disks is included.

The solutions are related through a complex parameter and Laplace equation solutions.

Abstract

The two known exact solutions of Einstein's field equations describing rotating objects of physical significance - a black hole and a rigidly rotating disk of dust - are discussed using a single mathematical framework related to Jacobi's inversion problem. Both solutions can be represented in such a form that they differ in the choice of a complex parameter and a real solution of the axisymmetric Laplace equation only. A recently found family of solutions describing differentially rotating disks of dust fits into the same scheme.