, Volume 66, Issue 2, pp 313–324

A new algorithm for anisotropic solutions

  • M. Chaisi
  • S. D. Maharaj


We establish a new algorithm that generates a new solution to the Einstein field equations, with an anisotropic matter distribution, from a seed isotropic solution. The new solution is expressed in terms of integrals of an isotropic gravitational potential; and the integration can be completed exactly for particular isotropic seed metrics. A good feature of our approach is that the anisotropic solutions necessarily have an isotropic limit. We find two examples of anisotropic solutions which generalise the isothermal sphere and the Schwarzschild interior sphere. Both examples are expressed in closed form involving elementary functions only.


Exact solutions anisotropic spheres superdense matter 


04.20.Jb 04.40.Dg 97.60.Jd 


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Copyright information

© Indian Academy of Sciences 2006

Authors and Affiliations

  • M. Chaisi
    • 1
    • 2
  • S. D. Maharaj
    • 1
  1. 1.Astrophysics and Cosmology Research Unit, School of Mathematical SciencesUniversity of KwaZulu-NatalDurbanSouth Africa
  2. 2.Department of Mathematics and Computer ScienceNational University of LesothoRoma 180

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