An analytic cylindrically symmetric solution for collapsing dust

TL;DR

This paper presents an exact analytic solution for the gravitational collapse of an infinite dust cylinder, revealing that topology is not fixed by Einstein's equations and connecting cylindrical symmetry with Friedmann interior solutions.

Contribution

It provides the first analytic interior solution for a cylindrically symmetric dust collapse, linking cylindrical symmetry to constant curvature Friedmann-like interiors.

Findings

The solution describes a collapsing dust cylinder with constant curvature interior.

Topology is not fixed by Einstein equations, allowing for different geometric interpretations.

The metric connects cylindrical symmetry with Friedmann interior solutions.

Abstract

Dust configurations are the simplest models for astrophysical objects. Here we examine the gravitational collapse of an infinite cylinder of dust and give an analytic interior solution. Surprisingly, starting with a cylindrically symmetric ansatz one arrives at a 3-space with constant curvature, i.e. the resulting metric describes a piece of the Friedman interior of the Oppenheimer-Snyder collapse. Indeed, by introducing double polar coordinates, a 3-space of constant curvature can be interpreted as a cylindrically symmetric space as well. This result shows afresh that topology is not fixed by the Einstein equations.