Exact Static Axially Symmetric Thin Annular Dust Disks

Details Exact Static Axially Symmetric Thin Annular Dust Disks Exact Static Axially Symmetric Thin Annular Dust Disks

2009-06-04

arxiv.org/abs/0906.0990v1

AIP Conf.Proc.1122:284-287,2009

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Physics and Mathematics of Gravitation: Proceedings of the Spanish Relativity Meeting 2008

Scientific paper

10.1063/1.3141294

A new family of exact solutions of the Einstein field equations for static and axially simmetric spacetimes is presented. All the metric functions of the solutions are explicitly computed and the obtained expressions are simply written in terms of oblate spheroidal coordinates. The solutions describe an infinite family of static axially symmetric thin annular dust disks. The disk are of infinite extension but with an inner annular edge. The energy densities of the disks are everywhere positive functions of the radial coordinate, equals to zero at the inner edge of the disk, having a maximun at a finite value of the radius and then vanishing at infinity. The disks have finite mass and their energy-momentum tensor agrees with all the energy conditions.

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