An analytic cylindrically symmetric solution for collapsing dust

Details An analytic cylindrically symmetric solution for collapsing dust An analytic cylindrically symmetric solution for collapsing dust

2004-09-27

arxiv.org/abs/gr-qc/0409096v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

8 pages, 1 figure

Scientific paper

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.

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