Abstract
An ansatz is developed to obtain interior solutions of the Einstein field equations for anisotropic spheres. This procedure necessitates a choice for the energy-density and the radial pressure. A class of solutions for a uniform energy-density source is presented. These anisotropic spheres match smoothly to the Schwarzschild exterior and are well-behaved in the interior of the sphere.
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Maharaj, S.D., Maartens, R. Anisotropic spheres with uniform energy density in general relativity. Gen Relat Gravit 21, 899–905 (1989). https://doi.org/10.1007/BF00769863
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DOI: https://doi.org/10.1007/BF00769863