Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2010-06-11
Mon.Not.Roy.Astron.Soc. 406:2689-2700,2010
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
22 pages, 7 figures, accepted for publication in MNRAS
Scientific paper
10.1111/j.1365-2966.2010.16863.x
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.
Letelier Patricio S.
Vogt Daniel
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