Journal Article

Newtonian and General Relativistic models of spherical shells – II

D. Vogt and P. S. Letelier

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 406, issue 4, pages 2689-2700
Published in print August 2010 | ISSN: 0035-8711
Published online August 2010 | e-ISSN: 1365-2966 | DOI: http://dx.doi.org/10.1111/j.1365-2966.2010.16863.x
Newtonian and General Relativistic models of spherical shells – II

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A family of potential–density pairs that represent spherical shells with finite thickness is obtained from the superposition of spheres with finite radii. Other families of shells with infinite thickness with a central hole are obtained by inversion transformations of spheres and of the finite shells. We also present a family of double shells with finite thickness. All potential–density pairs are analytical and can be stated in terms of elementary functions. For the above-mentioned structures, we study the circular orbits of test particles and their stability with respect to radial perturbations. All examples presented are found to be stable. A particular isotropic form of a metric in spherical coordinates is used to construct a General Relativistic version of the Newtonian families of spheres and shells. The matter of these structures is anisotropic, and the degree of anisotropy is a function of the radius.

Keywords: gravitation; galaxies: kinematics and dynamics

Journal Article.  3274 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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