General relativistic gravitational field of a rigidly rotating disk of dust: Solution in terms of ultraelliptic functions

TL;DR

This paper provides a complete analytic solution for the gravitational field of a rigidly rotating dust disk in general relativity using ultraelliptic functions, extending previous partial solutions.

Contribution

It introduces the full solution in terms of ultraelliptic functions and quadratures, advancing the analytical understanding of rotating dust disks in Einstein's equations.

Findings

Analytic expressions for the axis potential and disk metric

Complete solution in ultraelliptic functions

Enhanced understanding of rotating dust disk gravitational fields

Abstract

In a recent paper we presented analytic expressions for the axis potential, the disk metric, and the surface mass density of the global solution to Einstein's field equations describing a rigidly rotating disk of dust. Here we add the complete solution in terms of ultraelliptic functions and quadratures.